Assignment21a.R

factorial(5)

## [1] 120

factorial(0)

## [1] 1

choose(5,2)

## [1] 10

choose(5,2)*.5^2*.5^3

## [1] 0.3125

dbinom(2,5,.5)

## [1] 0.3125

dbinom(4,10,1/2)

## [1] 0.2051

dbinom(0,10,.5)

## [1] 0.0009766

dbinom(1,10,.5)

## [1] 0.009766

dbinom(2,10,.5)

## [1] 0.04395

dbinom(3,10,.5)

## [1] 0.1172

dbinom(0,10,.5)+dbinom(1,10,.5)+dbinom(2,10,.5)+dbinom(3,10,.5)

## [1] 0.1719

x=0:10
x

##  [1]  0  1  2  3  4  5  6  7  8  9 10

p=dbinom(x,10,.5)
p

##  [1] 0.0009766 0.0097656 0.0439453 0.1171875 0.2050781 0.2460938 0.2050781
##  [8] 0.1171875 0.0439453 0.0097656 0.0009766

plot(x,p,type='h',
     main="Binom(10,1/2)",
     xlab="Number of Heads",
     ylab="Probablilty",
     col="blue",
     lwd=2)

pbinom(3,10,.5)

## [1] 0.1719

dbinom(0,10,.5)+dbinom(1,10,.5)+dbinom(2,10,.5)+dbinom(3,10,.5)

## [1] 0.1719

x=0:10
p=dbinom(x,10,.5)

plot(x,p,type='h',
     main="Binom(10,1/2)",
     xlab="Number of Heads",
     ylab="Probability",
     col="green",
     lwd=2)

polygon(c(5.5,10.5,10.5,5.5),c(0,0,.27,.27),
        col=rgb(1,0,0,.3),border=NA)

polygon(c(-.5,5.5,5.5,-.5),c(0,0,.27,.27),
        col=rgb(0,0,1,.3),border=NA)

1-pbinom(5,10,.5)

## [1] 0.377

dbinom(6,10,.5)+dbinom(7,10,.5)+dbinom(8,10,.5)

## [1] 0.3662

x=0:10
p=dbinom(x,10,.5)
plot(x,p,type='h',
     main="Binom(10,.5)",
     xlab="Number of Heads",
     ylab="Probability")
polygon(c(-.5,8.5,8.5,-.5),c(0,0,.27,.27),
        col=rgb(1,0,0,.3),border=NA)

x=0:10
p=dbinom(x,10,.5)
plot(x,p,type='h',
     main="Binom(10,.5)",
     xlab="Number of Heads",
     ylab="Probability")
polygon(c(-.5,5.5,5.5,-.5),c(0,0,.27,.27),
        col=rgb(0,0,1,.3),border=NA)

x=0:10
p=dbinom(x,10,.5)
plot(x,p,type='h',
     main="Binom(10,.5)",
     xlab="Number of Heads",
     ylab="Probability")
polygon(c(5.5,8.5,8.5,5.5),c(0,0,.27,.27),
        col=rgb(0,1,0,.3),border=NA)

pbinom(8,10,.5)-pbinom(5,10,.5)

## [1] 0.3662

1-pbinom(54,100,.5)

## [1] 0.1841