2. (13 pts) Suppose that you repeatedly play a game where you roll a fair six-sided die. If the number of dots faces up

[answerhappygod]

2 13 Pts Suppose That You Repeatedly Play A Game Where You Roll A Fair Six Sided Die If The Number Of Dots Faces Up 1 (97.84 KiB) Viewed 32 times

2. (13 pts) Suppose that you repeatedly play a game where you roll a fair six-sided die. If the number of dots faces up is 6, you win $2; otherwise, you win $0. Let Så be the total amount that you win after n games. Assume S。 = 0. (a) Find E[S15], Var [S₁5], and Cç (15,20) = Cov(S15, S20). (b) Find the probability that you win $4 in 15 games, P[S15 = 4]. (c) Find a mathematical expression for P[S20 = 8|S15 = 4]. You do not need to evaluate it numerically. Just give an expression that could be evaluated numerically using Python or a calculator. (d) Find a mathematical expression for P[S20 = 8n S₁5 = 4]. (e) Now suppose that you start out with $5 (S = 5), but that each time you play the game costs you $1. What is the probability that you still have money after playing the game 8 times (Sg > 0)?