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dbinom(3,7,0.2)

## [1] 0.1147

##4.8##

#1#
hyper.x = 0:4
dhyper(hyper.x,6,6,4)

## [1] 0.0303 0.2424 0.4545 0.2424 0.0303

table = data.frame(hyper.x,dhyper(hyper.x,6,6,4))
colnames(table) = c( "X", "P(X)")
table

##   X   P(X)
## 1 0 0.0303
## 2 1 0.2424
## 3 2 0.4545
## 4 3 0.2424
## 5 4 0.0303

#2#
hyper.mean = sum(table[,1]*table[,2])/length(hyper.x)
hyper.mean

## [1] 0.4

tmp = (table[,1]-hyper.mean)^2
hyper.V = sum(tmp*table[,2])/(length(hyper.x)-1)
hyper.V

## [1] 0.8218

###4.9###

#1#
dpois(1,2.1)

## [1] 0.2572

#2#
1-ppois(3,2,1)

## [1] 0.1429

#3#
dpois(0,2.1)

## [1] 0.1225

###4.10###

dmultinom(c(1,2,3),prob=c(0.2,0.3,0.5))

## [1] 0.135

###4.11###

#1#
fail = 1-dnorm(97,mean=100,sd=6)

#2#
1-pbinom(2,5,fail)

## [1] 0.9982

#3#
fail.2 = 1-dnorm(106,mean=100,sd=6)
pbinom(1,3,fail.2)

## [1] 0.004748

###4.12###

#1#
pbinom(5,20,0.1) - pbinom(1,20,0.1)

## [1] 0.597

#2#
binom.mean = 20*0.1
binom.V = 20*0.1*0.9
binom.sd = sqrt(binom.V)
pnorm(5,mean=binom.mean,sd=binom.sd)-pnorm(2,mean=binom.mean,sd=binom.sd)

## [1] 0.4873

###4.13###

#1#
ppois(10,9)-ppois(6,9)

## [1] 0.4992

#2#
pois.mean = 9
pois.V = 9
pois.sd = sqrt(pois.V)

pnorm(10,mean = pois.mean, sd = pois.sd) - pnorm(7,mean = pois.mean, sd=pois.sd)

## [1] 0.3781

###4.14###
mean.14 = 3
sd.14 = 0.5

#1#
n.14=9
mean.14.1 = mean.14
sd.14.1 = sd.14/sqrt(n.14)

#2#
pnorm(2.5, mean = mean.14.1, sd = sd.14.1)

## [1] 0.00135