Question

Please answer in RStudio--> the Exercise 6.73 is unnecessary and the problem is stated below.

Answer 1

REQUIRED CODE

set.seed(4302019)
#part a)
x<-c()
for(i in 1:10000)
x<-c(x,min(runif(2)))
#part B)
hist(x,breaks = 10)
#part c) HERE CORRECT DENSITY IS 2*(1-X)
d<-c(0:50)/50
e<-2*(1-d)
hist(x,breaks = 10,probability = TRUE)
lines(d,e)
#part d)
mean_min<-mean(x)
var_min<-var(x)
print(mean_min)
print(var_min)
#theoritical mean is 0.33
#theoritical variance is 0.056

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R OUTPUT

> set.seed(4302019)
> #part a)
> x<-c()
> for(i in 1:10000)
+   x<-c(x,min(runif(2)))
> #part B)
> hist(x,breaks = 10)
> #part c) HERE CORRECT DENSITY IS 2*(1-X)
> d<-c(0:50)/50
> e<-2*(1-d)
> hist(x,breaks = 10,probability = TRUE)
> lines(d,e)
> #part d)
> mean_min<-mean(x)
> var_min<-var(x)
> print(mean_min)
[1] 0.3350795
> print(var_min)
[1] 0.05598781
> #theoritical mean is 0.33
> #theoritical variance is 0.056