The answer has to be a wellcommented code in RStudio a softw

The answer has to be a well-commented code in RStudio (a software package) Write a function that generates a multinomial distribution. For each trial we have m possible results. We will designate these outcomes by the integers from 1 to m. These outcomes are analogous to the outcomes of \"success\' and \"failure\" for a binomial random variable. The outcome of each trial is independent of the outcome of any other trial, and the probability of obtaining any of the m outcomes is identical for each trial. The function prototype is: r.multinomial p = c(0.3, 0.5, 1) > x = r.multinomial(10, 50, p) > x |1|, |, 2| |, 3| |, 4| |, 5| |, 6| |, 7| |, 8| I, 9| |, 10| |1, | 14 17 20 16 12 15 10 12 12 10 |2, | 7 14 7 14 9 5 17 13 10 8 |3, | 29 19 23 20 29 30 23 25 28 32 > colSums(x) |1| 50 50 50 50 50 50 50 50 50 50 > row Sums(x) |1| 138 104 258

Solution

r.multinomial <- function(n.out,n.trials,p)
{
res <- matrix(0,3,n.out);
for (i in 1:n.out)
{
samp <- runif(n.trials)
res[1,i]<-length(which(samp<=p[1]))
res[2,i]<-length(which(samp>p[1] & samp<=p[2]))
res[3,i]<-length(which(samp>p[2]))
}
return(res)
}

Sample Output:

> p<-c(0.3,0.5,1)

> ss<-r.multinomial(10,50,p)

> ss
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] 10 11 17 8 12 16 21 17 9 18
[2,] 10 12 6 7 12 8 7 8 6 11
[3,] 30 27 27 35 26 26 22 25 35 21

> colSums(ss)
[1] 50 50 50 50 50 50 50 50 50 50

> rowSums(ss)
[1] 139 87 274