library(ggplot2)

Tarea No. 3

En el siguiente ejercicio, crearemos una muestra de mil puertas, las cuales detràs de ellas tendremos un premio, los premios estaràn marcados con un signo positivo, mientras que las que tengan el signo negativo, seràn las puertas perdedoras.

puertas=sample(c(rep("+",60),rep("-",940)))
puertas
##    [1] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##   [19] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "-" "-" "-"
##   [37] "-" "-" "+" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##   [55] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-"
##   [73] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##   [91] "-" "-" "-" "-" "+" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [109] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [127] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "+" "-" "-" "-" "-" "-"
##  [145] "-" "-" "-" "-" "-" "+" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "-"
##  [163] "-" "-" "-" "-" "+" "+" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [181] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [199] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "-" "-" "-" "-" "-"
##  [217] "-" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "-" "+" "-" "-" "-" "+" "+"
##  [235] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [253] "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "-" "-" "-" "-" "-" "-"
##  [271] "+" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "-"
##  [289] "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "-" "-" "-" "-" "-" "-"
##  [307] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [325] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [343] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "+"
##  [361] "-" "+" "-" "-" "-" "-" "-" "+" "-" "-" "-" "-" "-" "+" "-" "-" "-" "-"
##  [379] "+" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "+"
##  [397] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "-" "-"
##  [415] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "-" "-" "-" "-" "-"
##  [433] "+" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [451] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [469] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [487] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [505] "-" "-" "-" "-" "+" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "-"
##  [523] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [541] "+" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [559] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [577] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [595] "-" "-" "-" "+" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [613] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "-"
##  [631] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [649] "-" "-" "-" "+" "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "-" "+" "-" "-"
##  [667] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "-" "-" "-" "-"
##  [685] "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [703] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [721] "-" "-" "+" "-" "-" "+" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "-"
##  [739] "-" "-" "-" "-" "+" "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "-"
##  [757] "-" "+" "+" "-" "-" "-" "-" "+" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [775] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "-" "-" "-"
##  [793] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [811] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [829] "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "-" "-" "+" "-" "-" "-"
##  [847] "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "-" "-" "-" "-" "+" "-" "-" "-"
##  [865] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "-" "-" "-" "-"
##  [883] "-" "-" "-" "-" "-" "+" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [901] "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "+" "-" "-" "+" "-" "-" "-" "-"
##  [919] "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "+" "-" "-" "-" "-" "-"
##  [937] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [955] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "-" "-" "-"
##  [973] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [991] "-" "-" "-" "+" "-" "-" "-" "-" "-" "-"

Aquì crearemos una funciòn en la cual obtengamos una muestra aleatoria de puertas donde sumemos la cantidad de puertas positivas que se obtengan en dicha muestra de tamaño n

puertas_win=function(n){
  muestra_puertas=sample(puertas,size = n)
  muestra_puertas_win=sum(muestra_puertas=="+")
  return(muestra_puertas_win)
  
}

Aquì le damos el tamaño a n y repetimos la operaciòn 5000 veces

puertas_win(n=100)
## [1] 4
winner=rep(NA,5000)

for (i in 1:5000) {
  winner[i]=puertas_win(n=100)
}

winner
##    [1]  6  3  8  6  7  8 12  7  5 10 12  5  5  7  6  5  7  5  6  3  7  8  6  3
##   [25]  7  8  3  7  4  7  5  5  8  3  3  6  7  4  7  5  6  6  7  9 12  7  6  6
##   [49]  5  3  7  6  8  6  5  5  6  9  3  5  5 11  5  9  5  8  2  6  5  9  4  7
##   [73]  8  4  5  5  5  5  5  4  6  7  8  1  6  5  3  3  6  5  4  9  3  8  8  5
##   [97] 12  6  7  5  6  5  5  8  4  7  7  2 11  2  5  5  1  6  6 10  6  8  7  7
##  [121]  8  4  7  5  6  6 10  7  9  6  7  4  5  3  6  6  9  8  6  5  7  6  8  6
##  [145]  8  6  7  8  4  5  5  7  2  8  7  6  8  5  4  5  9  7  3  7  7  9  4  7
##  [169]  8  7  6  6  8  9  4 10  9  8  6  2  5  4  6  6 11  7  6  9  6  3  5 10
##  [193]  8  5  8  9  7  5  8 10  4 11  6  5  7  2  2  6  4  4  8  7  5  5  7 10
##  [217]  6  3  4  3  7  6  3  3  7  8 12 10  6  7  2  7  8  4  5  5 12  3  4  2
##  [241]  3  6  3  3  8  7  6  5  8  7  7  5  5  5  4  7  9  1  5  7  2  7  6  7
##  [265]  4  5  5  6  7  5  9  2  7  8  5  6 11  3 10  7  9  6  9  5  8  8  5  2
##  [289]  4  6  5  7  5  2  4  6  6  7 11  9  6  6  9  7  6  7  6  4  8  3  7  3
##  [313]  5 12  5  5  4  4  4  6  7  2  7  3  3  5  3  6  4  8  6  7  2  6  7  6
##  [337]  3  6  6 10  5  9  4  4  5  6  4  8  4  8  5  8  3  9  8  7  9  8  8  3
##  [361]  4  9 11  5  6  7  6  9  9  6  5  9  4  5  6  5  5 10  4  8  6  2  7  4
##  [385]  5  8  6  6  5  7  4  4  8  6  3  7  9  6  1  5  4  7  5  9  9  9  6  3
##  [409]  7  3  5  5  4  5  7  7  9  5  4  6  5  9  7  7  9  5  6  7  6  5  8  5
##  [433]  7  2  8  3  8  4  6  3  5  5  6  4 10  6  5  3  3  5  9  7  6  8  5  8
##  [457]  7  7  6  9  3  7  4  7  7  6  6  6  7  6 12  8 11  8  5  4  4  5  7  2
##  [481]  7  7  4  6  3  7  6  6  6  6  4  6  6  5  7  6  4  5  6  9  3  8  7  6
##  [505]  5 10  7  9  7  6  7  9  7  9  6  5 13  4  5  1  7  5  6  7  8  7  6  3
##  [529]  7  3  5  8  6  3  8 11  2  6  5  6  9  4  7  4  7  4  4  7  2  5  5  5
##  [553]  7  1 10  3  3  9  3  4  8  4  4  2  4  5  7  5  4  4  7 10  8  3 11  3
##  [577]  7  7  6  6  3  7  7  9 10  9  3  3  6  4  6  5  6 10  8  7  3  4  5  9
##  [601]  7  6  8  5  3  2  8  9  5  6  8  4  7  5  8  5  9  7 10  4  7 11  8  6
##  [625]  5  7 11  8  8  8  8  6  4  7  5  4  4  4  8  8  2  3  6  4  7  4  8  5
##  [649]  4  4  9  6 11  5  5  2  2  7  4 10  5  4  7  8  6 10  7  3  8  6 10  3
##  [673]  6  3  3  8  6  5  5  2  5  5  7  5  5  5  4  7  6  8  7  5 11  5  4  4
##  [697]  5  5  7 11  6  2 10  3  5  6  6  4  7  7  7  5  3  5  6  4  6  7  8 12
##  [721]  8  7  6  6  7  6  7  4  7  4  2  3  5  6 11 11  5  8  8  5  7  5  5  5
##  [745]  6  5  2  5  5  9  7  4  3  7 13  5  8 11  7  2  6 10  4  5  3  5  6  5
##  [769]  5  8  4  6  6  3  9  4  6  7  7  5  3  8  7  5 12 11  6  5  6  6  7 10
##  [793]  3  7  4  6  3 11  7  4  7  5  9  4 10  7  7  6  4  5  7  4 10  7  7  4
##  [817]  6  3  7  6  4  5  5  7  6  6  9  9  4  8  0  6 11  6  3  5  2  9  5  7
##  [841]  5 11  9  6  5  9  3  5  4  8  4  5 11  5  5 10  9  5  8  2  7  7  7  5
##  [865]  9  7 12  8  8  5  4  5 10  7  6  2  4  5  6  5  7  5  8  8  8  5  3  4
##  [889]  1  5  5  8  5  5  7  8  6  7  7  5 10  5  3  5 12  1  6  5  4  5  7 10
##  [913]  3  4  7  6  6  9  2 10  8  9  6  6  6  5  3  9  9  4  8  9  8  9  3  6
##  [937]  9  6  6  5  6  7  5  8  4  5  7  5  4  6  6  9  8  8  9  4  5  5  8  7
##  [961]  8  6  5 10  6 10  9  3  7  3  2  7 10  7  9  5  8  5  2  6  4  7  2  6
##  [985]  5  6  8  9  8  5  6  7  2  7  6  3  5  6  5  9  6  4  6  3 12  4  5  5
## [1009]  8  7  7  4  6  9  4  2  5  7  5  6  6  6  4  5  6  8  9  2  5  5  5  7
## [1033]  4  5  7  7  3  7  9  4  7  7  8  7  3  7  6  2  9  4  6  4  8  2  7  8
## [1057]  2  3  7  7  4  6  6  3  8  6  4  5  8  5  8  4  7  9  6  7  7  7  4  9
## [1081]  6  4  5  6 10  6  8  7  8  4  7  0  6  2 10  6  4  4  5  5  6  7  5  7
## [1105]  5  4  8  6  5  3  6  9  3  6 12  9  9  8  5  3  8  6  5  7  7  7  6  7
## [1129]  3 13  4  6  6  5  7  5  7 10  5  6  8  7  6  8  8  6  3  7  8  3  5  4
## [1153]  5  8  8  8  8  6  5  5  8  9  6  4  5 12  6  7  8  6  9  3  7  8  7  8
## [1177]  6  4  9  6  7  9  6 14  5  5  7  7  8  6  8  6  7  5  5  4  5  3  4  6
## [1201]  6  6  6  5  6  8  3  5  8  7  8  6  3  6  9  5  5  6  3  2  4  7  8  6
## [1225]  5  5 10  4  5  5 10  5  7  5  4  5  7  3  6  9  7  7  4  6  4 10  6  8
## [1249]  5  5  5  4  8  5  4  5  3  8  5  5  7  5  8  9  5  8 10  9  3  5  2  6
## [1273]  3  4  6  5  6  8  4  3  5  6  4  4 10  3  3  3  9  8  4  8  5  8  8  4
## [1297]  4  3  8 11  8  5  6  7  7  8 10  8  5  5  8  8  6  7  6  5  3  6  2  5
## [1321]  4  1 10  9  4  5  6  7  5  9  6  3  7 10  5  7  8  5  5  5  4  8  7  8
## [1345] 13  9  9  7  6  8 10  6  7  3  6  5  4  2  3  9  9  2  4  7  8  4  8  4
## [1369]  8  4  4 11  8  6  2  6  8  9  6 10  6  3  6  6  6  8  3  5  9  7  4  4
## [1393] 10  5  6  6 11  5  4 10  6  5  6  7 10  7  8  5  7  4  6  5  2 11  6  8
## [1417]  8  8  8  6  4 10  4 10  4  6  7 10  7  9  7  3  7  7  6  6  8  6  7  4
## [1441]  5  4  4  9  9  4 10  9 10  2  4  7  6  9  6  1  8  2  6  6  8  5  8  5
## [1465]  2  5  5  9  6  5  5  2  9  7  5  3  6  8  1  9  4  7  8  6  3 11  6  4
## [1489]  5  3  4  5  7  3  8  6  9  4  5  5  4  2  9  8  4 10  2  8  6  9  1 10
## [1513]  4  7  4  3  8  9  5  4  7  4  9  4  7  5  8  9  3  4  5  7  7  2  8  6
## [1537]  7  6  5  5  6  8 12  5  6  2  6  7  8  9  8  4  7  5  8  7 10 11  6  7
## [1561]  3  5  3  4  7  5  8 11  9  5  9  3  6  5  7  3  7  7  9  4  6  5  3  8
## [1585]  2 13  4  3  2  8  5  4 10  3  6  4  5  9  3  7  5  5  9  5  4  5  7  7
## [1609]  9  7  7  5  6  2  4  5 12  4 11  5  9  4  3  8  4  7  4  6  2  6  5  6
## [1633]  6  5  8  6  7  9  5  7  9  9  3  5  7  8  6  8  6  7  6  8  2  4  8  7
## [1657]  9  3  3  6  5  6  4  8  8  6  6  4  5  8  6  3  7  4  1  7  3  7  6  6
## [1681]  8  8  4  8  5  9  5  5  6 12  8  6  8  9  3  3  4 10  4  9  8  7  5  7
## [1705]  2  6  6  8  8  9 10  6  7  6  6  9  9  6 13  5  7 13  7  9  5  8  3  8
## [1729]  7  5  6  4  3 10  7 10  6  5  8  7  5  7  6  4  8  9  7  2  6  4  9  7
## [1753]  6  5  7  5  3  8 11  3  9  3  9  4  3  1  4  4 10  9  7  5  5  7  4  3
## [1777]  4  6  5  8  3 11  4  7  4  8  6  7  5  6  5  4  5  5  4  5  6  8  5  4
## [1801]  4 12  6  4  8  4  6  3  4  6  3  5  5 13  3  4 10  6  6  4 10  7  3  6
## [1825]  9  5 10  3  8  4  8  6  3  6  5  7  9  8  5  3  7  3  2  7  6  9  6  2
## [1849]  9  6  4  5  8  6  8  6 10  8  3  7  6  6  4  7  6  7  6  4  8  4  7  5
## [1873]  7  5  8  6  0  5  5  4  5  7  7  7  5  7  9  5  7  8  7  6  8  4  9 11
## [1897]  6  9  7  6  4  8  5  6  5  6  6  9  6 10  4  6  6  9 10  3  7  5  1  4
## [1921]  7  3  6  9  4  3  3  9  6  3  6  6  8  4  5  4  7  5  2  2  6  7  8  5
## [1945]  4  7  3  6  7  9  5  4 10  4  5  7  7  8  3  7  6  7  8  4  9  3  6  7
## [1969]  6  5  5  9  5  3  9  3  6  3  4  5  6  2  6  6  3  7  3  5  4  5  9  6
## [1993]  7  7  5  7  4  6  6  7  7  6  7  7  6  1  6  5  4  7  6  9 10  9  3  9
## [2017]  5  5 10  7  9  2  8  8  5  4  3  9  7  7  7  4  4  6  4  7  4  9  5  5
## [2041]  6  7  3  9  3  5 10  6  7  9  6  6  4  3  9  3  6  7  6  4  4  4  3  5
## [2065]  4  8  8  9  5  6  5  5  4  4  4  0  5  7  6 11  8  4 11  5  3  2  5  6
## [2089]  7  6  6  9 10  7  4 11  5  7  4  9  6  1  5  5 12 10  6  7  6  4  6  5
## [2113]  4  1  7  4  4  8  4  7  8  3  6  7  4  6  5  4  5  6  6  5  2  5  3  6
## [2137]  5  5  4  2  4  7  3  6  7  7  2  5  3  5  5  5  4  5  4  6  6  5  7  5
## [2161]  5  5  7  4  8  7  5  5  4  8  4  8  6  6 10 10  6  5  5  4  5  5  7  8
## [2185] 11  4  5  1  6  5  6  4  5  5  8  4  5  3  3  5  8  7  2  4  4  4  6  4
## [2209]  7  9  5  3  8  9  4  8  8 11  4  3  6 11  6  6  2  4  5  4  7  6  7 11
## [2233]  5  6  5  9 13 10 12  6  6  8  9  8  4  3  8  8  4  5  7  4  1  3  5  7
## [2257]  7 10  6  3  2  4  5  5  8  3  9  7  8  4  9  8  6  6  9  2  5  9  6  4
## [2281]  7  8  5  4  4  7  0  6  3 11  7  7  6  7  4  8 11 10  1  5 11  9  7  4
## [2305]  5  8  8  4  4  8  6  6  7 11  9  9  8  5  8  4  4  4  3  8  4  6 10  7
## [2329]  5  7  6  2  4  5  9  7  6  9  3  6  4  8  3  6  4  7  4  7  7  8  8 10
## [2353]  6 11  3  4  2  5  5  5  5  3  7  7  6  5  5  9  5  6  6  4 11  4  3 10
## [2377]  3  5  3  2  4  6  7  4  3  5  7 10  5  4  7  3  7  6  4  6  9  4  5  6
## [2401]  5  7  5  9  6  5  9  5  6  4  7  4  9  3  5  2  5  6  4  8  6  6  6  6
## [2425]  6  7  6  4  5  5  6  6  8  6  8  5  6  7  4  4  4  2  5  6  8  4  3  3
## [2449]  8  4  6  5  4  4 12  7 12  8  7  5  8 10  6  7  1  6  4  7  8  7  3  8
## [2473]  6  3  2  6  8  3  7  4  3  5  6  6  6  3 10  7  6  2 11  5  7  6  4  4
## [2497]  6  5  7  7  9  7  6  6  7  6  4  4  3  7  6  8  7  7  4  4  5  4  5  5
## [2521]  8  2  5  4  7  6  6  5  7  8  6  8  2  5  5  5  7  9  4  4  7  4  7  5
## [2545]  4  6  5  5  8  7  9  7  5  5  9  6  5  5  4  5  5  6  8  1  8  5  5  8
## [2569]  7  6  6  4  6  4  7  5  5  7  3  8  5  6  5  3  7  3  2  4  9  3  2  5
## [2593]  7  5  8  9  4  9  4  4  6  7  6  6  5  4  5  9  6  4  7  5  3  6  6  8
## [2617]  6  2  7  7  4  5  3  5  3  5  5  6  3  6  8 10  5  6  5  7  9  3  6  3
## [2641]  5  5  5  7  9  5  5  5  2  6  5  4  6 11  5  4  3  5  6  4  7  2  6  9
## [2665]  6  6  5  7  6 10  5  5  6  6  6  3  6 12 10  5  7 11  5  9  5  6  9  3
## [2689]  7  9  7  5  5  2  6  6  7  5  4  6  3  9  8 10  4 15  7  5 11  7  8  5
## [2713]  7 12  6  9  6  7  9  2  5  5  9  8  4  6  4  8  3  4  6  8  7  3  4  7
## [2737]  5  3  4  9  7  7  7  6  9  3  7  7  5  3  7  4  4  7  3  7  5  4  8  2
## [2761]  7  7  5  6  8 10  9  5  5  4  6  8  4  6  9  7  5  3  8  6  2  8  7  4
## [2785]  5  5  2  6  6  8  7  2  6  1  6  7  3  7  1  4 10  6  7 10  8  3  1  4
## [2809]  2  4  4  3  4  4  6  7  8  4  5  2  4  2  8  6  9  4  9  4 11 10  5  5
## [2833]  9  7  4  6  2  5  7  5 10  5  4  5  4  7  5 10  6  9  8  2  8  7  3  5
## [2857]  7  5  2  7  4  4  7  3  7  7  6  5  6  5  7  9  6  5  2  6  5  5  6  7
## [2881] 10  7  7  4  5  5  5  5  6  8  3  6  5  5  4  5  5  7  6  7  9  4  4  6
## [2905]  6  8  9 12  5  4  1  4  6  5  4 10  5  6  6  6  5  4  7  7  6  6  8  5
## [2929]  8  7  3  5  6  6  5  4  7  2  5  6  5  8  5  8  2  9  5  2  3  9  4  8
## [2953]  7  6  6  7  5  9  7  5  4  6  9  6  7 12  5  6  5  6 10  6 13  4  3  5
## [2977] 10  7  9  6  7  8  3  9 10 10  5  7  4  5  8  1  8  4  6  7  5  6  6  2
## [3001]  6  8  7  6  7  4 12  4  9  8  9  4  3 10  8  4  5  5  8  6  4 10  6  6
## [3025]  5  6  2 10  8  6  1  5 10  7  6  6  7  4  8  7  6  4 11  7  9  3  5  7
## [3049]  6  8  3  6  8  6  3  9  5  3  3  7  3  6  6  7  5  4  8 10  3  5  5  7
## [3073]  8  7  6  3  5  7  9  7  3  5  3  5  7 10  5  4  6  8  6  5  6  4  5  8
## [3097]  6  7  4 10  3  8  7  4  6  6 10  3  9  7 11  6  6  5  6  5  7  9  2  8
## [3121] 12  7  6  3  7  8  7  5  6  4  6  6  1 10  8  5  2  8  4  6  4  8  4  5
## [3145]  7  4  6  6  6  5  6  6  6  5  8  4  9  5  5  8  4  4  5  5  9  3  4  7
## [3169] 10  2  8  8  7  5  5  6  7  4  6  8  4  7  3  5  6  5  7  7  6  5  4  3
## [3193]  5  7  7  5  6  7  3  6  5  4  8  5  8  7  7  4  2  6  9  6  3  5  3  9
## [3217]  7  9  4  6  6  3  6  8  3  4  6  4  5  6  9  9  6  6  3  1  6  8  3  8
## [3241]  6  6  7 10 11  9  7  9  8  5  6  5  7  6 11  4  5  7  8  5  4  6  4  5
## [3265]  5  5  6  5 11  9  6  8  7  4  9  8 11  7  2  5  2  8  7  5  3  9  4  4
## [3289]  4  3  7 10  5  6  5  2  6  2  6  7  4  3  6 10  4  6  3  6  7  7  6  7
## [3313]  8  8  7  5  4  5 11 10  3  6  2  7  6  4  8  9  7  6  7  6  4  6  7  4
## [3337]  7  6  6  1  7  3  7  9  4  7  6  8  8  8  5  9  5 11  5  5  5  4  8  3
## [3361]  2  6  8  6 10  6  9  4  7  4  8  5  8  4 10  4  8  8  6  8  3 10  8  2
## [3385]  8  5  5  3 12  8  6  4  8  4  5  7  5  4  4  3 10  7  8  6  6 11  4  3
## [3409]  1  2  3  7  5  3 10  4  7  2  3  7  7  7  6  8  6  7  6  5  5  4  5  7
## [3433]  7  5  6 10  4  6  6  8  5  7  4  8  8  9  5  7  8  6  8  7  5  8  3  4
## [3457]  5  3  5  6  6  7  4  3  7  3  6  8  2  3  7  8  8  3  6  4  8  6  5  7
## [3481]  5  3  7  5  6  6  2  6  7  1  7  7  9  9  5 10  5 11  7  9  4  2  5  5
## [3505]  4  7  5  6  7  9  6  8  5  3  7  5  6  5 12  6  8  4  4  8  7  6  6  2
## [3529]  7  5  3  5  8  9  4  8  7  6  5  7  2 10  3  5  3  3  5  7  9  8  6  4
## [3553] 14  2  9  5  5  9  4  6  1  7  6  7  6  4  2  4  7  3  6 10  5  8  8  8
## [3577]  6  5  5  3  7  4  8  2  4  9 13  8  7  6  4  6  8  5  6  7  5  4  4  4
## [3601]  5  6  5  6  7  8  8  3  4  6 13  5  6  7  1  5  8  7  2  5  6  4  6  6
## [3625]  7  6  4  5  9  7 10  6  6  3  5  8  4  2  5  3  6  6  7  8  5  5  6  4
## [3649]  9  8  8 12  8  9  3  4  5  8  5  5  6 10  8 10  7  7  2  2  6  9  5  4
## [3673]  6  3 10  6  6  2  5 10  6  6 10  8  5  4  3  7  7  6  9  5  4  5  4  6
## [3697]  6 11  3  8  6  6  6 12  3  8  7  5  6 10  5  5  7  6  4  7  4  4  4 10
## [3721]  5  7  4  7  4  4  9  8  7  3  4  6  4  5  7  7  1  9 10  6  4  1  8  3
## [3745]  2  2  2  5  8  4  6  7  3  3  7  2  3  4  7  3  4  7  2  7  3  7  1  6
## [3769]  6  5  6  4  9  3  4  8  5  2  6  8  8  3  7  3  6  5  8  5 10  5  3  8
## [3793]  7  6  4  6  6  3  4  2  7  5  4  7  6  7  6  3  4  5 10 10  5  8  5  3
## [3817]  6 12 10  6  8  3  7  5  8  3  9  7  5  8  6  8  6  5  5  9  7  3  4  5
## [3841]  6  6  7  7  7  5  8  8  9  8  2  7  7  7  5  6  8  6  9  8  3  5  7 10
## [3865]  4  5  6  3  6  4  2  9  5  5  3  7 10  8  4  4  6  4  6  4  2  4  7  4
## [3889]  4  4  9 11  6  6  6  8  7  1 11  4  2  0  9  8  3  5  5  5  4  5  5  6
## [3913]  4  4  5  6  8  6  8  4  8  5  6  9  9  8  9  9  8  2  6  9  6  7  5  5
## [3937]  4  7  6  7  3  6  5  6  6  5  7  5  8  5  4  2  8  8  4  4  7 10  7  6
## [3961] 10  8  4  5  4  7  3 10  6 10  6  7  5  9  4  5 10  5  4  5  6  6  7  4
## [3985]  7  9  7  7  4  7  5  7  4  5  4 10 10  8  7  4  5  8  5 11  7  4  7  5
## [4009]  4  5  8  5  7 10  3  5  6  5  7 10  6  6  4  9  4  6  4  1  9  5  8  8
## [4033]  4  4  4  8  1  9  7  6  4  8  8  3  4  9  9  6  2 11  4  3  5  5  8  5
## [4057]  5  3  2 12  7  5  6  3  5  4  4  3  3 10  5  6  6  4  7  5  5  9  1  7
## [4081]  7  5  2  5  4  3  5  6  7  6  6  7  5  9  9  4  4  7  6  9  5  6  6  4
## [4105]  8  5  4  5  5  8  2  4  4  7  4 11  6  8  4  4  3  6  6  4  8  4  8  5
## [4129]  9  7  5  5  4  1  8  7  6  8  5  4  7  3  6  3  6  5  7  5 10  7  4  4
## [4153]  5  5  5  6  7  4  4  6  7  6  8  6  7  5  7  5  8  7  6  6  4  8  9  8
## [4177]  4  7  4  4  2  6  2  3  4  5  8  8  6  5  2  7  4  3  6  6  4  9  4  3
## [4201]  5  3  8  5  4  3  8  8  5  7  6  4  4 13  6  9  4  3  6  7  4  3  5  6
## [4225]  5  5  7  8  5  9  5  5  6  6  8  9  4  9  9  6  3  4  6  7  5  6  6  5
## [4249]  4  5  7  1  9  6  5  7 10  7  6  5  8  5  4  3  9  4 11  2  3  6  2 10
## [4273] 10 10  7  4 10  5  7  5  5  8  7  2  6  5 11  5  7 10 12  4  5  3  3  5
## [4297]  5  9  8  3  3  5  7 10  5  2  6  7  4  3  6  5  7  7  7  6  2  6  3 10
## [4321]  9  7  4  7  6  6  4  5  4  7  5  5  5  9 10  3  2  5  4 10 10  7  6  9
## [4345]  8  5  8  8  6  4  1  4  7  6  7  8  4 10  8  8  9  5  7  7  4  5  5  2
## [4369]  6 11  5  5  7  9  8  7  5  3  5  4  6  8  6  6  5  3  6  9 10  5  8  4
## [4393]  4  3  6  5  6  6  7  4  5  8  4  9  5  9  8  6  7  7  4  4  5  6  4  5
## [4417]  5  4  4  8  6  3  7  1  5  1  5  8  6  8  5  7  5  6  7  5  5 10  7  7
## [4441]  5  6  8  7  4  2  7  5  5  8  8 10  1  3  5  4  8  8  5  5  5  5  4  5
## [4465]  3  7  7  5  7  5  6  9 10  5  5  7  3  6  7  6  6  8  4  7  7  3  6  6
## [4489]  3  9  6  6  4  4  5  4  9 10  8  7  5  6  7  4  3  8  4 12  6  6  6  6
## [4513] 13  5  3  4 10  8  6  6  5  9  6  6  4  9  5  8  4  2  6  6  5  8  6  6
## [4537] 11  6  3  5  8  4  7  5  6  8  9  9  6  7  4  4  4  6  7  7  5  3  7  7
## [4561]  9  3  7  8  4  9  7  8  5  6  4  4  8  4  8  5  7  4  4  6  5  7  4  6
## [4585]  4  2  8  5  5  4  6  3  5  7  4  7  3  5  9  5  4  8  5  4  7  4  5 10
## [4609]  3  9  6  5  4  7  6  4  3  1  6  7  6  9  6  9  7  4  7  9  6  9  5 10
## [4633]  7  7  9  7  5  8  5  3  8  4  9  5  3  9  4  5  3  6  3  9  8  8  9  8
## [4657]  6  9  5  3  9  4 10  6  2  7  8  9  6  8  7  6  7  7  8  8 11  4  7  5
## [4681]  8  3  4  2  3  5  9  2  7  5  3  9  9  6  3  7  0  4  4  8  6  2  4 10
## [4705]  3  6  5  6  4  6  6  9  8  3  5  8 11  5  5  6  3  3  9  4  5  8  1  9
## [4729]  3  4  5  6  7  8  6  6  4  5  9  8  2  7  7  8  8  8  6  9  5  4  5  6
## [4753]  2  5  5  6  9  4  8 12  8  7  5  7  6  7  8  5 10  9  6 10  4  7  5  7
## [4777]  6  7  2  6  9  3  4  3  4  2  5  2  4 11  5  4  9  6  6 10  5  6  3  5
## [4801]  4 12  7  8  5  8  2  5  4  7  5  4  6  9  5  7 10  3  8 12  4  6  4  6
## [4825]  8  4  5  6  8  8  7  6  6  4  7  7  5  6  6  9  2  6  4  7  6 10  4  8
## [4849] 11  6  6 10 11  8  8  5  7  5  4  6  5  3  9  8  4  6  2  5  8  9  8  5
## [4873]  6  6  6  4  7  5  8  6  3  8  9  4  4  3  8  9 10  6  5  6  7  4  3 10
## [4897]  6  9  5  5  6  4  5  4  8  6  4  3  7  8  5  2  8  5  5  8  3  6  5 11
## [4921]  9  6  5  9  4  6  6  5 10  2  5  8  7  4  7  5  2  5 12  5  8  5  3  6
## [4945]  5  4  6  8  9  5  4  4  5  6  6  2  7  5  7  5  5  5  3  4  3  7  3  6
## [4969]  6  4  4  6  5  8  6 12  5  4  6  3  2  3  4  9  3  4  6  6  4  4  8 10
## [4993]  6  3  9  6  8  6  6  6
mean(winner)
## [1] 5.9758

Posteriormente observamos con un histograma el comportamiento normal que se obtiene de los datos.

casos=as.data.frame(winner)

figura=ggplot(data=casos,aes(x=winner))
figura+geom_histogram(binwidth = 0.5)

Repetimos el mismo ejercicio pero cambiando el porcentaje de puertas ganadoras, ya no es un 6%, sino un 30%. Mas posibilidades de ganar.

maspuertas=sample(c(rep("+",300),rep("-",700)))
maspuertas
##    [1] "-" "-" "+" "-" "-" "-" "+" "-" "-" "+" "-" "+" "-" "+" "-" "+" "-" "-"
##   [19] "-" "+" "-" "-" "-" "-" "+" "-" "-" "+" "-" "+" "+" "+" "-" "-" "+" "+"
##   [37] "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "+" "-"
##   [55] "-" "+" "+" "-" "-" "-" "-" "-" "+" "+" "-" "-" "+" "-" "+" "-" "-" "-"
##   [73] "+" "-" "-" "-" "-" "+" "+" "-" "+" "+" "+" "-" "-" "-" "-" "+" "-" "-"
##   [91] "-" "-" "+" "-" "-" "-" "-" "-" "-" "+" "+" "+" "+" "+" "-" "-" "-" "+"
##  [109] "-" "-" "+" "-" "-" "+" "+" "-" "-" "-" "-" "+" "-" "-" "-" "-" "-" "-"
##  [127] "+" "+" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "-" "-" "-" "-" "-" "-"
##  [145] "-" "-" "+" "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "+" "-" "-" "+" "-"
##  [163] "-" "+" "+" "-" "-" "+" "-" "-" "+" "-" "-" "+" "+" "-" "-" "-" "-" "-"
##  [181] "-" "+" "+" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "-"
##  [199] "-" "-" "-" "-" "-" "+" "-" "-" "+" "-" "+" "-" "-" "+" "-" "-" "-" "+"
##  [217] "-" "-" "-" "+" "-" "-" "-" "+" "-" "-" "-" "-" "-" "+" "+" "+" "-" "+"
##  [235] "-" "+" "-" "-" "+" "+" "+" "-" "-" "-" "-" "+" "-" "-" "-" "-" "-" "-"
##  [253] "+" "-" "-" "+" "+" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "-" "-" "-"
##  [271] "-" "-" "-" "-" "-" "+" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "+" "-"
##  [289] "-" "+" "+" "-" "+" "-" "-" "-" "+" "-" "-" "+" "-" "-" "+" "-" "-" "-"
##  [307] "-" "+" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "-" "-" "-"
##  [325] "-" "+" "-" "+" "-" "-" "-" "+" "+" "-" "-" "-" "-" "-" "+" "+" "-" "-"
##  [343] "+" "-" "-" "-" "+" "+" "+" "-" "+" "-" "-" "-" "-" "+" "-" "+" "+" "-"
##  [361] "-" "+" "+" "-" "-" "-" "-" "-" "-" "+" "-" "-" "-" "-" "-" "+" "-" "-"
##  [379] "-" "-" "-" "+" "-" "-" "+" "+" "-" "+" "-" "-" "-" "-" "-" "-" "-" "-"
##  [397] "-" "-" "-" "+" "-" "-" "-" "+" "-" "-" "-" "+" "-" "+" "+" "+" "-" "+"
##  [415] "-" "-" "-" "+" "-" "-" "-" "+" "+" "+" "-" "-" "-" "+" "+" "-" "-" "-"
##  [433] "-" "-" "+" "-" "+" "+" "-" "-" "+" "-" "+" "+" "-" "+" "+" "-" "+" "-"
##  [451] "+" "+" "-" "+" "-" "-" "+" "-" "+" "-" "-" "+" "-" "-" "-" "+" "-" "-"
##  [469] "-" "-" "-" "-" "-" "-" "-" "+" "+" "-" "-" "-" "-" "-" "-" "-" "-" "-"
##  [487] "-" "+" "+" "-" "+" "-" "-" "-" "+" "-" "-" "+" "-" "-" "-" "-" "-" "-"
##  [505] "+" "-" "+" "+" "-" "-" "+" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "-"
##  [523] "-" "-" "+" "-" "-" "-" "-" "+" "-" "+" "-" "-" "-" "-" "-" "-" "-" "-"
##  [541] "-" "+" "+" "-" "-" "+" "-" "+" "-" "-" "-" "+" "+" "-" "-" "+" "+" "-"
##  [559] "+" "-" "-" "-" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "+" "-" "-" "-"
##  [577] "-" "+" "+" "+" "-" "+" "+" "-" "-" "+" "-" "+" "+" "-" "-" "-" "-" "-"
##  [595] "+" "-" "-" "-" "-" "-" "-" "+" "+" "+" "-" "+" "-" "-" "-" "-" "-" "-"
##  [613] "-" "-" "+" "-" "+" "-" "-" "+" "-" "-" "-" "+" "+" "+" "-" "+" "-" "-"
##  [631] "+" "-" "-" "-" "-" "-" "-" "+" "-" "-" "+" "+" "-" "+" "-" "-" "-" "+"
##  [649] "-" "-" "+" "-" "+" "+" "-" "-" "+" "-" "-" "-" "-" "+" "+" "-" "-" "-"
##  [667] "+" "-" "-" "-" "-" "-" "+" "-" "-" "-" "-" "-" "+" "+" "-" "-" "-" "-"
##  [685] "-" "-" "-" "-" "+" "-" "+" "-" "-" "-" "-" "+" "-" "-" "+" "-" "-" "-"
##  [703] "-" "+" "-" "+" "-" "-" "-" "-" "-" "-" "+" "-" "-" "-" "-" "+" "-" "+"
##  [721] "-" "-" "-" "+" "-" "-" "+" "-" "+" "-" "+" "-" "-" "-" "+" "-" "-" "+"
##  [739] "-" "-" "-" "-" "-" "-" "+" "-" "-" "+" "-" "-" "-" "-" "-" "-" "-" "+"
##  [757] "+" "-" "-" "+" "-" "-" "-" "-" "-" "+" "+" "-" "-" "-" "+" "-" "-" "+"
##  [775] "+" "-" "-" "+" "-" "-" "-" "+" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-"
##  [793] "+" "-" "-" "-" "-" "-" "-" "+" "+" "+" "-" "-" "+" "+" "-" "-" "+" "-"
##  [811] "+" "+" "-" "-" "-" "-" "+" "+" "-" "+" "+" "+" "-" "-" "+" "+" "+" "-"
##  [829] "-" "-" "-" "-" "-" "-" "-" "-" "+" "-" "-" "-" "-" "+" "-" "+" "-" "-"
##  [847] "-" "-" "+" "-" "-" "+" "+" "+" "-" "-" "+" "-" "-" "-" "-" "-" "+" "+"
##  [865] "-" "+" "-" "-" "-" "-" "-" "+" "-" "-" "-" "-" "+" "-" "+" "-" "-" "-"
##  [883] "-" "-" "-" "-" "-" "-" "+" "+" "-" "-" "-" "+" "-" "-" "+" "-" "-" "-"
##  [901] "-" "-" "-" "-" "+" "+" "-" "-" "+" "-" "-" "-" "+" "-" "-" "+" "+" "-"
##  [919] "-" "-" "-" "+" "-" "-" "-" "-" "+" "+" "+" "-" "-" "-" "+" "+" "+" "+"
##  [937] "+" "-" "+" "-" "-" "+" "+" "-" "-" "-" "-" "-" "-" "+" "-" "+" "-" "-"
##  [955] "-" "-" "+" "-" "-" "+" "-" "+" "-" "-" "-" "-" "+" "-" "+" "-" "-" "-"
##  [973] "-" "-" "+" "+" "+" "-" "+" "-" "-" "-" "+" "-" "-" "-" "+" "-" "-" "-"
##  [991] "+" "+" "-" "+" "+" "-" "+" "+" "-" "-"
maspuertas_win=function(n){
  
  muestra_maspuertas=sample(puertas,size = n)
  muestra_maspuertas_win=sum(muestra_maspuertas=="+")
  return(muestra_maspuertas_win)
}
maspuertas_win(n=100)
## [1] 4
maswinner=rep(NA,5000)

for (i in 1:5000) {
  maswinner[i]=maspuertas_win(n=100)
}

maswinner
##    [1]  4  2  5  8  5  6  8  5  5  5  8  6  8  6  7  3  5 10  7  4  5  7  3  5
##   [25]  4  5  7  6  6  4  3  7  8  8  3  6  2  5  7  6  3  3 10  7  6  5  4  5
##   [49]  6  7  9  7  6  9  7  4  3  4  4  2  4  5  5  8  3  5  8  7 11  2  6  7
##   [73]  4  6  8  9  8  5  7 10  5 10  6  2  4  7 10  8 10  7  5  6  9  4  6  5
##   [97]  4  4  3  8  4  7  8 11  3 11  6  5  3  5 10  7  6  5  5  6  7  6  7  5
##  [121]  2  2  7 10  3  5  4  3 11  4  6  8  4  5  8  3  7  6 12  6  5  3  7  7
##  [145]  5  4  8  3  3  5  8  6  5  7  7  9  9  5  7  6  4  9  4  6  4  7  7  4
##  [169]  4 10 10  6  6  5  5  5  5  7  6  8  6  6  5  4  4  6  3  5  6  8  5  6
##  [193]  3  6  8  3  3  2  7  5  6  8  3  5  7  6  6  3  2  6  5  6  7  7  7  9
##  [217]  5  6  8  6  7  6  3 12  6  8  7  6  6  7  5 10  7  7  5  7  4  3  7  9
##  [241]  4  4  7  5  5  7  6  5  5  7  7  8  5  7  5  9  5  8  6  5  5  4  7 11
##  [265]  7  9  4  5  9  7  3  7  5  7  7  8  3  3  4  6  7  4  7  2  7  7 10  9
##  [289]  5  2 11  4  2  6  5  9  7  3  4  3  9  5  5  8  9 11  8  6  2  6  8  9
##  [313]  6  5  7  8  8  4  9 12  8  5  4  5  6  7  5  5  8  3  3  5  5  5  8  3
##  [337]  4  7  5  9  8  6  7  3  8  5 10 10  6 11  9 11  6  5  7  5  5  6  5  8
##  [361] 10  6  7  2  7  5  6  3 10  6  5 12  6  5  7  3  7  5  4  2  8  7  9  6
##  [385]  3  8  7  5  6  6  4  4  5  2  2  4  1  6 10  7  6  5  6 13  6  8  6  8
##  [409] 10  5  6  6  7  2  2  4  3  7  9  9  7  5  5  6  5  8 11  7  7  7  3  7
##  [433]  5  5  5  5  6  3  7  7  6  3  8  6  6 12  5  8  7  5 11  2  5  5  5  5
##  [457]  8  3  5  7  5  5  8  8  8  5  4  6  2  2  4  6  9  4  4 12  8  8  4  4
##  [481]  5  5  4  6  3  4  6  7  5 10  3  8  4  8  6  6  6 13  7  3  2  6  3  7
##  [505]  6  3  7  6 10  5  6  6  8  8  6  6  7  7  9  3  8  5  2  7  4  8  6  4
##  [529]  8  1  6  9  9  5  6  8  3 11  7  4  6  4  8  5  5  7  7  5  6  6  8  6
##  [553]  6  7  7  4  6  9  8  6  1  7  7  3  6  6  5  8  8  4  5  6  5  5  3  6
##  [577]  4  4  7  7  4  3  8  6  8  5  7  6  8  7  7  4  8 10  5  5  5  6  5  8
##  [601]  7  3  7  7  9  6  9  4  7  4  8  5  6  9  4  7  6  4  7  6  6  6  2  4
##  [625]  9  6  6  5  5  5  8  4  6  7  5 12  6  5  7  7  6  1  4  0  9 10  6 11
##  [649]  5  8  5  9  7  4  5  4  6  5  5 12  8  6  4  9  9 12  9  3  6  7 10  6
##  [673]  6  9  8  8  8  6  2  3  5  4  5  4  2  7  6  7  5  5  5 10  3  9  3  6
##  [697]  8  4  5  6  8  5  9  7  7  5  3  7  9  7  9  5  5  7  9  7  7  4  5  5
##  [721]  6  5  1  7  5  2  8  9  9  3  5  4  9  5  4  2  6  8  3  5  7  7 10  3
##  [745]  6  5  4  6  7  5  8  6  7  8  9  4  4  4  2  4  3  5  6  7  5  4  3  7
##  [769]  6  6  4 10  4  5 13  6  4  3  4  3  5  7  7  2  3  4 10  9  1  7  5  7
##  [793]  9  8  7  8  5  6  6  6  9  3  4  6  7 11  6  2  2  3  7  7  8  6  7  8
##  [817]  7  6  6  4 10  4  4  5  5  6  6  3  7  5  6  6 10  5  9  7  3  6  5  4
##  [841]  7  4  9  7  4  6  8  5  6  9  7  5  5  3  7  8  4  8  8 12  9  4  5  2
##  [865]  3  6  6  6  7  3  7  8  4  9  4  4  6  7  7  4  8  7  6  4  9  5  6  6
##  [889]  5  4  9  6  5 12  4  5  7  5  4  6  6  6  2  2  7  7  6 10  6  7  4  5
##  [913]  5  7  4  7 11  4  4  7  7  7  9  6  8 13  5  7  7  5  4  6  3  4  5  4
##  [937]  5  7  4  6 10  5  4  5  1  4  9  9  6  2 13  7  9  4  7  4  5  9  6 10
##  [961]  6  7  6  4  5  7  7  6  7  7  9  7  4  7  5  7  6  5  7  6  7  9  6  3
##  [985]  5  4 10  7  3  4  9  3  3  6  6  3  6  7  9  5 10  7  1  5  7  6  6  5
## [1009]  4  6  5  8  3  7  6  6  4  7  4  5  8  5  6  4  7  3  4  9  4  4  6  9
## [1033]  5  7  5  4  7 10  5  3  9  6  6  6  6  5  7  6 11  8  6  7 12  4  6  6
## [1057] 11  5  8  4  3  5  8  5  8  4  3  6  7  6  8  5  3  2  7  8  6  6  3  7
## [1081]  6  5  6  7  9  9  7  8  5  8  9  8  9  6  5  9  6  7  5  2  5  7 10  9
## [1105]  4  5  9  9  6  3  7  8  9  6  7  4  3  5  5  5  4  5  3  3  4  4  4  7
## [1129]  6  6  8  5  5  7  3  7  6  3  4  8  2  8  7  7  5  6  7  6  9  5  3  8
## [1153]  4  8  6  6  9  5  2  6  4  3  6  9  2  7  8  6  2  6  4  8  4  7  6  5
## [1177]  7  7  2  7  7  6  8  7  9  6  8  6  8  9  9 10 13 11  5  7  6  3  5  6
## [1201]  3  6  7  2  4  7 10  6  4  8  3  8  7  5  7  8  4 11 11  3  7  9  6 10
## [1225]  6  9  6  4  6  7  2  6  5  7  8  4 12  4  9  6  8  5  9  2  5  7  8  7
## [1249]  9  6  4  4  8  8  8  6  6  7  7  8  5  3 10  8  5  6  4  7  4  6  5  6
## [1273]  8  3  2  6  2  5  7  6  7  5  2  4  7  5  6  7  6  9  4  7  9  4  6  4
## [1297]  3  7  2  9  5  5  5  7  7  5  4  5  4  5  7  4  8  8  5  8  6  5  5  7
## [1321]  8  5  7  6  6 10  5  3  8  5  4 10 12  7  9  9  7  8  8  7  4  5  4  5
## [1345] 10  2  7  5  8  4  4  5  4  6  9  4  8  3  4  9  6  3  2  9  8  7  7  5
## [1369]  7  8  6  4  4  9  8  7  5  6  7  3 10  9  7  5  5  8  8  8  4  4  6  8
## [1393]  3 10  4 10  6  7  1  6  8  7  4  8  8  7  7  9  7  7  6  6  5  8  6  5
## [1417]  6  5  2  2  6  7  4  6  7 11  5  8  8  4  4  6  3  6  7  7  6  3  7  6
## [1441]  6  7  9  6  2  6  6  6  6  6  5  5  7  5  7  6  9  5  6  7  1  8  5  6
## [1465]  3 12  5  7  5  6  3  6  7  9  8  4  6  7  3  7  6  6 10  9  4  5  5  8
## [1489]  4  6  6  9  3  3  5  5  5  7  5  6  6 10  5  4  8  6  4  8  9  8  5  5
## [1513]  3  7  6  5  3  5  8  3  6  9  5  3  5  5  3  7  3  4  7  8  5  8  5 12
## [1537]  8  2  4  5  7  8  2  9  8  6  4  9  8  7  8 10  5  6  6 10  2  7  7  5
## [1561]  5  4  6  6  2  8  5  7  4  7  6  3  6  3  9  2  5  4  2  3  8  6  5  5
## [1585]  5  6  7  6 11 11  4  5  6  4  3  2  3  6  4  1  5  5 13  5  4  5  9  6
## [1609]  4  3 11  9  6  8  4  4  5 10 11  3  7  5 10 11  9  9  8  4  5  7  8  6
## [1633]  5  5  7  7  8  6  8  5  6  8  7  4  2  6 10  6  5  2  6  4  3  8  5  3
## [1657]  8  8  6  9  9  8  6  4  5  5  7  5  7  7  3  6  7  9  4  4  3  6  2  5
## [1681]  5  8  4  5  8  6  7  9  5  3  1  7  8  5  9 10  9  5  4  9  9  5  7  7
## [1705]  4  6 10  7  5  5  7  5  3  5  4  6 11  6  9  5  7  8  7  8  6  4  8  5
## [1729]  5  5  7  7  5  1  7  7  7  3  9  6  5  6  5  7  8  8  6  6  6  7  9  3
## [1753]  6  3  6  5  6  8  8  6  7  6  6  7  7  4  9 11  6  8  4  7  7  7  5  6
## [1777]  5  6  9  9  5  8  8  7  7 11  8  6  6  5  4  6  5  5  7  3  8  4  6  9
## [1801]  5  4  7  6  7  7  7  8  4  5  5  5  4  4  9  7  2  5  3  9  7  6  9  9
## [1825]  2 10  4  5  6  5  4  4  5 11  4  6  5  5  6  8  8  9  4  7  7  3  4  4
## [1849]  4  6  5  6  6  7  6  3  4  3  6  6  7  4  5  6  6  6  2  5  7  2  6  7
## [1873] 10  3  6 12  5  8  6  6  5  7 12  8  6  6 13  6 10  4  5  4  8  5  9  5
## [1897]  3  7  6  5  5  4  7  7  7  9 13  5  8  7 10  6  2  8  8  6  3  7  5  5
## [1921]  8  4 11  6  5  6  5  5  5 10  9  6  7  8  4  4  5  7  6  8  5  3  8  5
## [1945]  4  5 10  6  6  5  6  4  6  5  7  8  4  9  4  6  4  6  4  4  5  7  7  6
## [1969]  7  5  8  3  6 14  5  5  7  9  6  8  8  5  5 12  4  5  8  7  6  7  7  6
## [1993]  9  3 14  6  8  4 12  7  8  5  8  5  5  7  4  5  8  8  9  7  5  5  4  9
## [2017]  5  6  6  8  3  4  4  9  4 12  5  4  2  6  8  7  9  9  5  7  4  4  1  3
## [2041]  6  8  5  5  6  5  8  9  4  6 11  9  5  4  5  6  4  8  8  4  8  6  6  6
## [2065]  5  5  3  7  4  7  4  2  4  3  7  9  6  3  8  3  3  4  9  9  5  7  5  4
## [2089]  6  8  3  8  5  1  7  3  4  6  5  7  6  5  3 10  6  3  4 10  4  4  7  3
## [2113]  6  3  9  8  6  7  5  6  1  9 12  5  3  5  2  9  5  3  3  7  9  5  5  4
## [2137]  3  7  4  3  4  4 10  4  8  7  8  5  9  6  4  9  3 10  4  5  3  6  7  2
## [2161]  9  6  5  8  7  6  8  4  7  4  4  5  5  5  8  5  2  2  4  8  4  3  2  6
## [2185]  8  5  4  7  5  6  5  5  5  8  7  7  6  5  9  6  4  3  8  5  6  7  4  7
## [2209]  9  2 10  7  3  9  6  7  6  5  7  6  7  7  8  6  3  5  5  5  5  8 10  7
## [2233]  6  5  7  5  3  5  3  5  8  7  5  9  6  8  7  2  9  7  9  5  6  7  7  7
## [2257]  6  5  3  6  6  2  5  7  2  8  3  9  3  9  5  9  4  4  3 14  6  4  4  4
## [2281]  8  9  5  9  5  9  7  4  7  7  6  5  7  3  4  6  8  6  8  3  4  4  6  7
## [2305]  8  6  4  5  5  5  9  4  9  5  5  6  6  8  0  2 10  7  9  8  5  3  8  4
## [2329]  7  7  5  6  5  5  7  6  6  4  6  4  8  2  7  9  4  7  3  6  8  5  5  8
## [2353]  4  5  9  7  6  6  8  7  6  5  8  3  6  7  9  7  4 11  7  8  7  6  3  7
## [2377]  6  2  6  8  5  3  5  9  7  9  8  4 10  8  6  8 10 13  7  4  7  3  7  8
## [2401]  7  6  5  8  3  5  5  4  9  2  9  8  5  6  9  9  7  4  6  3  7  4  3  4
## [2425]  7  4  4  0  4  7  3 10  7  7  6  7  8  5  8  4  7  5  7  6  8  9  4  6
## [2449]  6  8 11  6  6  4  6  5  4  5  6  4  6  4  8  5  7  8  9  1  5  6  3  8
## [2473]  6  5  7  9  6  6 10  7  5  3  7  8  6  4  4  5  5  4  8  6  7  5  6  8
## [2497]  2  8  5  5  6  6  7  7  5  1  9 10  5  3  4  7  6  8  8  6  8  7  6  6
## [2521]  6  7  6  5 10  9  6  2  4  6  7  5  4  9  2  9  8  7 14  3  6  8  5  3
## [2545]  8 11  4  5  6  8 12 10  3  3  4  3  5 10  7  4  6  3  6  8  9  4  1  6
## [2569]  7  5 10  1  6  2  8  7  4  4  6  6  4  7 11  2  4  3  6  7  4  4 12  6
## [2593] 10  5  6  7  3  4  9  3  4 10  4  5  5  2  4  5 10  7  6  3  5 10  8  6
## [2617] 14  3  3  3  6  6  6  8  5  5  5  6  9  7  4  7  5  8  3 11  4  5  6  3
## [2641]  5  7 12  8 11 14  4  6  7  5  7  8  5 11  6  9  5  3  5  4  5  5  6  4
## [2665]  8  5  3  6  6 10  4  7  7  7  4  5  7 10  9  4  4  5  5  7  3  6  2  6
## [2689]  6  6  5  7  4  1  6  5 10  5  6  6  9  6  8  7  8  4 11  3  4  3  7  7
## [2713]  8  5  4  7  4  4  8  5  8  3 10  7  6  4  3 10  1 13  6  8  9  7  4  3
## [2737]  5  8  4  9  6  3  3  7  3  6  9  4  3  7  4  6  9  8  7  8  7  3  4  6
## [2761]  1  7  3  5  7  3  6  4  4  5  3  6  9 10  7  6  7  9  8  5  6  4  6 10
## [2785]  5  5  8  5  7  6  6  5  7  3  6  5  5  9  9  5  4  7  5  7  9  2  5  5
## [2809]  5  7  4  2  9  3  4  4  5 10  6  2  5  6  8  8  5  4  5  6  5  4  8  7
## [2833]  4 11  5  8  3  6  6  4  7  8 12  5  7  3  6  5  5  6  8  5  3  7  7  8
## [2857] 10  4  6  9  8  3  8  5  5  6  8  8  4  4  6  9  8  8  5  4  8  4  5  7
## [2881] 10  6  7  4  4  9  5  8  5  3  6  6  5  7  5  5  6  8  7  3  3  4  7  4
## [2905]  4  6  7  8  2  5 10  6  7  4  3  7  7  3  5  6  8  5  5  4  7  4  4  6
## [2929]  6  7 10  6  4  4 10  5  4  6  4  8  3  6  6  5  7  6  8  7  6  6  7  4
## [2953]  7  6  4  6 11  3  2  6  4  4  9 11  3  6  5  6  7  6  3  8  4  6  4  3
## [2977]  5  6  4  6  8  4  4  5  6  7  3  7  3  4  6  4  6  6  6  9  4  7  2  6
## [3001]  8  5  2  7 11  4  2  4  8  4  5  5  9  7  6  4  7  4  5  4  7  6  5  6
## [3025]  5  8  5  8  6  8  3  2  6  3  7  8  7  4  7  4  6  9  7  8  7  5  6  7
## [3049] 11  4  8  5  9  5  3  5  8  4  8  8  7  6  7  5  5  8  3  6  3  7  4  7
## [3073]  9  6 10  5  2  3  4  4  9  3  6  5  4  3  6  4  8  8  6  6  9  7  4  3
## [3097]  3  5  9  5  4  4  7 10  2  7  8  8  5  5  6  6  7  8  7  4  7  5  4  2
## [3121]  6  4  7  9  5 12  6  6  4  9  5  2  6  6  6  5  7  8  7  6  4  8  4  6
## [3145]  3  2  7  5  5  6 12  6  8  9  5  9  7  4  5  6  6  8 10  6  5  6  9  7
## [3169]  9  4  2  7  5  8  4  4 11  2  9  5  2  2  7  3  4  4  9  5  4  7 12  9
## [3193]  5  6  6  7  2  5 12  5  7  6  8 10  4  9  2  6  4  6  6  6  4  6 10  5
## [3217]  4  8  7  3  7  7  5  5  6  8  7  6  7  5  7  9 10  5  4  4  3  6  9  3
## [3241]  9  3  4  8  6  6 10  6  7  5  5  4  2  7  6  9  3 11  6  4  8  6 10  3
## [3265]  7  6  7  5  7  6  9  3  4  5  7  6  6  4  5  3  3  4  7  7  8  8  7  5
## [3289]  4  9  3  8  8  7  5  4 14  6  7  8  3  7  9  4  7  5  6  8 12  4  5  8
## [3313]  7  8  3  3  4  5  7  8  2  9  7  5  1  6  6  5  6  7  7  5  9  6  6  8
## [3337] 13  9  6  5  5  5 11  4  2  6  5  4  7  5  6  5 10  4  6  4  7  9  4  4
## [3361]  6  6  4  4  4  9  5  4  8  6  8  6 11  3  5  8  4  8  4  7  5  9  7  2
## [3385]  4  7  5  6  8  5  6  5  3  7  3  4  6  5  8  2  6  3  5  8  7  4  6 12
## [3409]  5  6  8  6  4  6  7  7  6  8  8  4  5  7 15  5  6  6  5  1  3  6  6  8
## [3433]  7  7 12  6  3  3  3  7  6  3  8  5  6  6  8  8  9  7  6  7 10  7  4 10
## [3457]  6  1  3  9  1  5  7  7  2  9 10  3  6  6  4  6  4  4  3 11  9 10  5  6
## [3481]  4  8 10  6  4  8  7  5  4  7  8  8  8 10  6  8  8  1  2  7  6  2  6  6
## [3505]  3  5  6  5  5  6  9  8  8  8  8  8  8  6  9  4  5  2  2  9  6  5  8  8
## [3529]  7  8 11  3  3  6  8  5  5  2  6 10  2 10  9  6  7  3  4  9  6  6  5  7
## [3553]  5  7  4  5  6  6  8  8  9  5  5  5  4  6  6  5  5 10  6  6  6  5  4 11
## [3577]  6  9  8  8  3  5  3  7  3 11  4  8  6  8  8  9  5  9  7  8  9  3  8  2
## [3601]  3  6 10  6  6  1  3  6  4  5 10  9  5  6  6  4  6  5  5  4  4  4  5  7
## [3625]  4  5  6  6  5  7  6 10  8  5  6  8  7  4 10  5  3  5  9  7  4  5  5  6
## [3649]  6  7  5  8  5  6 10  9  7  7  5  5  8  7  5  5  4 10  8  4  6  7 10  8
## [3673]  5 11  6  3  7  4  7 10  3  9  9  6  8  6  8  2  2  8  8  7  9  3  4  6
## [3697]  6 10  4  9  8  7  8  3 12  8  8  4  5  5  6  5  8  2  8  8  3  6  8  3
## [3721]  8  5  9  8 11  8  4  9 10 10  9  7 11  6  5  8  6  4  6  7  5  9  5  9
## [3745]  5  8 10  9  6  4  8  6  7  7 10 11  5  5  7  8  6 12 12  3  7  4  6  5
## [3769]  5  5  7  6  2  9  7 10  7  4  3  7  8  7  3  6  4  4  7  6  7  8  5  8
## [3793]  8  8  1  7  7  1  7 10 11 12  4  7  5  3  1  6  6 12  4  5  4  8  3  6
## [3817]  4  5  5  8  7  2  8  1  8 10  4  6  5 10  8  7  5 10  6  3  5  6  3  8
## [3841]  8  5  6  6  4  7  5  7  4  4  3  9  5  8  6  6  4  4  7  8  4  8  3  8
## [3865]  7  8  7  5  8  9  7  7  3 11  5  8  8  8  8 10  6 10  2  5  3  9  6  4
## [3889]  6  3  4  7  5  4  8  8  6  7  6 13  7  3  9  6  7  8  7  6  8 13  8  8
## [3913]  4  9  8  6  5  5  2  8  4  5  4  2  7  6  8  5  6  6  5  5  8  3  8  7
## [3937] 11  5  4  5  7  3 10  7  5  7  3  7  2  6  5  8  5  8  7  8  4  5  8 11
## [3961]  5  6  5 10  7  8  2  6  9  4  8  8  4  5 10  3  3  3  6  7  4  6  5  3
## [3985] 10  6  4  7  7  6  8  6  7  5  7  6  6  7  4 10  4  8  4  5  3  6  6  7
## [4009]  6  7  7  6  7  7  4  7  9  6  5  4  7  3  4  8  3  5 13  4  9 11  1  5
## [4033]  7  7  8  6  5  2  8  4  9  3  5  6  8  7  8  8  5  8  5  7  3 10  3 12
## [4057]  5 12  8  8  6  5  9  9  8  6  9  3  7  5  8  6  4  7  5  4  8  5  7  3
## [4081]  5  3  6  5  5  6  5 10  8  4  7  9  6  5 10  7  3  9  9  6  3  6  8  7
## [4105]  6  2  7  6  7  9  6  6  4  4  6  6  5  4  8  7 10  4  7  3  5  6  1  7
## [4129]  6  5  9  3  7  6  3  7  7  3  6  3  6  3  8  7  5  6  7  2  5  4  5  8
## [4153]  3  6  5 10  8  9  6  9  8  3  5  7  5  7  5  7  7  7  6  7  6  6  6  5
## [4177]  7  9  5 13  9 11  8  7  7  2  4  9  8  6  5  6 11  4  5  4  5  2 10  9
## [4201]  5  7  7  5  8  9  8  7  6  5  8  8  5  5  6  9  3  5  9  5  6  5  4  7
## [4225]  5  6  9  3  8  4  4  5  1  3  7  6  2  8  4  3  4  7  4  5  6  7  6  4
## [4249]  4  7  4  4  7  6  8  5  7  7  6  8  5  7  7  6  4  3  9 12  8 10  5  8
## [4273] 10  7  8  5  5  8  7  8  5  5  5  7  9  7  8  9  5  3  4  8  6  3  9  3
## [4297]  6  8  5  4  8  5  9  1  8 10  3  9  9  7  6  6  8  5  8  6  8  6  5  6
## [4321]  8  4  3 10  5  6  6  6  5  3  6  5  5  3  6  3  6  8  7  7  6  4  4  6
## [4345]  9  3  8  4  7  4  7  8  7  5  5  5  3  8  5  6  7  7  5  5 10  8  8  5
## [4369]  4  9 10  5  5  4  3  6  6  4  6  7  3  8  5  4  7  3  3 10  8  5  6  6
## [4393]  6  6  3  5  5  5  7  7  3  4  4  7  5  5  6  6 10  4  8  7  6  3  5  7
## [4417]  5  5  5  3  3  4  6  6  6  8  5  9  5 10  4  9 10  5  6  4  3  5  4 11
## [4441]  7  5  4  5  8  7  6  8  7  8  9  7  8  7  4  6  3 11  3  5  3  4  8  6
## [4465]  6  8  4  8  4  8  6  7  5  5  4  5  8  4  8  2  5  5  3  5  4  6  2  5
## [4489]  5  5  8  4  8  4  5  3  7  7  7  2  7  4  6  5  3  7  4  5  6  6 11  7
## [4513] 10  9  7  8  6 10  6 12  6  3  3  1  6  8  8  7 10  7  2  4  7  9  3  7
## [4537] 10  7  5  6  5  4  6  6  7 11  7  3  5 10 11  4  4  5  1  8  1  9  8  5
## [4561]  6  2  9  6  6  5  6  2  6  7  7  2  7  4  6  4 10  9  3  5  4  2 13  5
## [4585]  7  8  6  6  5  5  6  7  7  0 10  5  7  8  9  2  2  8  5  8  6  4  5 12
## [4609]  8  4  4  3  8  6  5 10  8  7  4  5  3  5  7  6  7  7  4  8  5 10  7  8
## [4633]  6 10  4  4  5  4  7  8  8  6  4  5  8  8  3  6  3  7  5  8  6  5  8  5
## [4657]  8  3  5  7  6  5  9  7  3  5  5  7  8 12  6  2  4  5  6  8  6  7  1 12
## [4681]  4  8  5  6  7  7  7  6  5 10  8  8 10 10  5  8 10  7  7  4  5  5  5  4
## [4705] 10 11  9  7  7  7  7  3  5 11  6  4  8  4  5  5  4  3  4  9  8  5 12  9
## [4729]  7 13  6  7  5  3  7  7  5  5  5  9  3  6  9  7  9  7  6  3  6  2  4  8
## [4753]  7  6  2 10  8  6  7  3  8  4 11  6  7  5  7  6  4  7  7  4  8  4  2  9
## [4777]  6  5  4  7  8  5  3  7  7  9  5  7  7  6  6  1  7  6  5  9  7  4  5  7
## [4801]  9 10  4  5  6  5  4  5  6  6  6  7 10  9  6  9  4 10  4  4  5  4 11  4
## [4825]  6  8  2  6  8  3 10  6  8 12  5  6  3 11  8  4  7  6  6  6  6  4  8  7
## [4849]  6  7  5  4  8  5  3  5  5  7  7  2  6  8  6  6  7  2  3  6 11  5  6  5
## [4873]  7  9  8  3  3 10  3  5  3  9  8  3  7  4  6  4  7  7  5 12  6  8  7  5
## [4897]  9  5  6  4  6  3  3  4  6  8  4  4  7  4  9  7  4  7  7  4  6  5  2  4
## [4921]  4  8  9  5  5  5  9  4  5  5  3  6  8  5  6  8  3  5  4  9  7  9  5  4
## [4945] 11  7  6  8  9  8  6  5  6  4 11  7  3  4  7  6  2  8  5 11  5  5  6  9
## [4969]  1  1  9  5  4  9  6  9  5  4  5  7  6  7  6  6  7  5  8  7  5  8  7  8
## [4993]  8 10  9  4  2  4  8  6
mean(maswinner)
## [1] 6.0628
mascasos=as.data.frame(maswinner)

figura=ggplot(data=mascasos,aes(x=maswinner))
figura+geom_histogram(binwidth = 0.5)