Number Game Subject:

Number Game

Subject: Discrete Maths and Probabilities (CS 70)

Sinho and Vrettos are playing a game where they each choose an integer uniformly at random from [0,100], then whoever has the larger number wins (in the event of a tie, they replay). However, Vrettos doesn't like losing, so he's rigged his random number generator such that it instead picks randomly from the integers between Sinho's number and 100. Let S be Sinho's number and V be Vrettos' number. 

(a) What is E[S]?

(b) What is E[V|S = s], where s is any constant such that 0 ≤ s ≤ 100?

(c) What is E[V ]?