Answers to Lab Session 2, Simulating Experiments

Task 2:
It estimates the probability P(X<cutpoint) where X is an exponential 
random variable with rate equals rate (1 as the default).

Task 3:
lab2.task3 <- function()
{
  N <- sum(sample(0:1,4,replace=T))
  if (N<2) {
    Y <- sample(1:6,1,replace=T)
  } else {
    Y <- max(sample(1:6,2,replace=T))
  }
  X <- sum(rexp(Y,2))
  return(X)
}

Task 4:
lab2.task4 <- function(N=10000)
{
  counter <- 0 
  for (i in 1:N) {
    X <- lab2.task3()
    if (X>3) {
      counter <- counter + 1
    }
  }
  return(counter/N)
}

The required probability is approximately 0.220.