Question

3 a) Suppose that we wish to generate observations from the discrete distribution with probability mass function 2)+1 20 x=1,2, 3, 4, 5 Clearly describe the algorithm to do this and give the random numbers corresponding to the following uniform(0,1) sample. 0.5197 0.1790 0.9994 0.6873 0.7294 0.5791 0.0361 0.2581 0.0026 0.8213 NB: Do not use R for this part of the question. two numbers rolled. Write an R function which will generate n random rolls of a pair b) Consider the problem of rolling two fair dice and reporting the sum of the sum of the

Answer 1

R code:

n<-10000
samp<-c()
a<-0
for(a in 1:n)
samp<-c(samp,sum(sample(c(1:6),2,replace = T)))
hist(x = samp)
#observed probability
table(samp)/n
#exact probability
rbind(2:12,c(1:6,5:1)/36)
# yes they are matching verified

OUTPUT

> source('~/.active-rstudio-document', echo=TRUE)

> n<-10000

> samp<-c()

> a<-0

> for(a in 1:n)
+ samp<-c(samp,sum(sample(c(1:6),2,replace = T)))

> hist(x = samp)

> #observed probability
> table(samp)/n
samp
2 3 4 5 6 7 8 9 10 11 12
0.0297 0.0566 0.0818 0.1111 0.1407 0.1638 0.1389 0.1081 0.0840 0.0576 0.0277

> #exact probability
> rbind(2:12,c(1:6,5:1)/36)
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 2.00000000 3.00000000 4.00000000 5.0000000 6.0000000 7.0000000 8.0000000
[2,] 0.02777778 0.05555556 0.08333333 0.1111111 0.1388889 0.1666667 0.1388889
[,8] [,9] [,10] [,11]
[1,] 9.0000000 10.00000000 11.00000000 12.00000000
[2,] 0.1111111 0.08333333 0.05555556 0.02777778

> # yes they are matching verified