Question

1. Consider the R code

n <- 10000

sample<-rbinom(1,size,prob=0.2)

proportion <-sample/n

1. Describe what the line containing rbinom does.
2. 1/proportion will, with high probability, be close to a particular whole number.  Which one? Give justification for your answer, including the names of any standard results that you use.

Answer 1

a.

The second line should be sample<-rbinom(1,size = n,prob=0.2)

rbinom creates a Binomial random variable of parameter n = 10000 and p = 0.2

b.

We know that for large sample size, n, the binomial distribution will approximate normal distribution with mean = np = 10000 * 0.2 = 2000

Also, the mean occurs with the high probability and thus sample = 2000 will have the highest probability.

proportion = sample / n = 2000 / 10000 = 0.2

Thus, 1/proportion  with high probability is 1/0.2 = 5