Find answers to the following questions by simulation using SAS (at least 10000 simulations). You must provide a final answer once you have observed the output from SAS and give reasons for your answers.That is, if there is convergence, why and what is the final answer. However, if there is divergence, why.

1. Suppose X_ifor i=1, 2, 3... has uniform (0, 1) distribution.

1. Let M = min (n: X₁+ X₂+ ... + X_n> 1). Find expected value of M; E(M) = Mean of M.
2. Let N = min (n+1: X_n> X_n+1). Find expected value ofN; E(N) = Mean of N.

2. A one unit stick is broken randomly into two pieces.

1. Find E (the short piece divided by the long piece).
2. Find E (the long piece divided by the short piece).