library(gtools)
library(knitr)
1.
x <- c(6,7,8,9,10,11,12,13,14)
ninios <- c(37369, 87436, 160840, 239719, 286719, 306533, 310787, 302604, 289168)
n = sum(ninios)
prob.x <- ninios/ n
x
## [1] 6 7 8 9 10 11 12 13 14
prob.x
## [1] 0.01848875 0.04325998 0.07957747 0.11860378 0.14185758 0.15166079 0.15376551
## [8] 0.14971687 0.14306925
2.
v.e <- sum(x * prob.x)
v.e
## [1] 10.99913
3.
prob.acum.x <- c(sum(prob.x[1]), sum(prob.x[1:2]), sum(prob.x[1:3]),
sum(prob.x[1:4]), sum(prob.x[1:5]), sum(prob.x[1:6]),
sum(prob.x[1:7]), sum(prob.x[1:8]), sum(prob.x[1:9]))
prob.acum.x
## [1] 0.01848875 0.06174874 0.14132621 0.25992999 0.40178757 0.55344837 0.70721387
## [8] 0.85693075 1.00000000
4.
tabla <- data.frame(1:9, x, prob.x, prob.acum.x, x * prob.x, (x - v.e) ^ 2, (x - v.e) ^ 2 * prob.x)
colnames(tabla) <- c("pos","x", "prob.x", "prob.acum.x", "x.prob.x", "x-v.e^2", "x-v.e^2prob.x")
kable(tabla)
| 1 |
6 |
0.0184888 |
0.0184888 |
0.1109325 |
24.9912583 |
0.4620571 |
| 2 |
7 |
0.0432600 |
0.0617487 |
0.3028199 |
15.9930068 |
0.6918572 |
| 3 |
8 |
0.0795775 |
0.1413262 |
0.6366198 |
8.9947553 |
0.7157799 |
| 4 |
9 |
0.1186038 |
0.2599300 |
1.0674340 |
3.9965038 |
0.4740005 |
| 5 |
10 |
0.1418576 |
0.4017876 |
1.4185758 |
0.9982523 |
0.1416097 |
| 6 |
11 |
0.1516608 |
0.5534484 |
1.6682687 |
0.0000008 |
0.0000001 |
| 7 |
12 |
0.1537655 |
0.7072139 |
1.8451861 |
1.0017493 |
0.1540345 |
| 8 |
13 |
0.1497169 |
0.8569307 |
1.9463193 |
4.0034977 |
0.5993912 |
| 9 |
14 |
0.1430693 |
1.0000000 |
2.0029696 |
9.0052462 |
1.2883739 |
5.
barplot(height = tabla$prob.x, names.arg = tabla$x)
6.
plot(x,prob.acum.x, type = 'b')
7.
var <- sum((x - v.e) ^ 2 * prob.x)
var
## [1] 4.527104
8.
desv.std <- sqrt(var)
desv.std
## [1] 2.127699
Probabilidades
kable(tabla[,1:4])
| 1 |
6 |
0.0184888 |
0.0184888 |
| 2 |
7 |
0.0432600 |
0.0617487 |
| 3 |
8 |
0.0795775 |
0.1413262 |
| 4 |
9 |
0.1186038 |
0.2599300 |
| 5 |
10 |
0.1418576 |
0.4017876 |
| 6 |
11 |
0.1516608 |
0.5534484 |
| 7 |
12 |
0.1537655 |
0.7072139 |
| 8 |
13 |
0.1497169 |
0.8569307 |
| 9 |
14 |
0.1430693 |
1.0000000 |
9.
i=5
i = min(tabla$x) - 1
i
## [1] 5
tabla$prob.acum.x[7-i]
## [1] 0.06174874
cat(tabla$prob.acum.x[7-i] * 100,"%")
## 6.174874 %
10.
1 - tabla$prob.acum.x[8-i]
## [1] 0.8586738
11.
tabla$prob.acum.x[11-i] - tabla$prob.acum.x[8-i]
## [1] 0.4121222