(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 S0. Let S, be the total amount that you win after n games. Assume S, = 0. (a) Find E[S4s], Var[S15), and C,(15, 20) = Cov(S15,Sz0). (b) Find the probability that you win $4 in 15 games, P[Sis 4]. (c) Find a mathematical expression for P[S20 = 8|S;5 = 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 Sis = 4). (e) Now suppose that you start out with $5 (So = 5), but that cach time you play the game costs you $1. What is the probability that you still have money after playing the game 8 times (S, > 0)?
(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 S0. Let S, be the total amount that you win after n games. Assume S, = 0. (a) Find E[S4s], Var[S15), and C,(15, 20) = Cov(S15,Sz0). (b) Find the probability that you win $4 in 15 games, P[Sis 4]. (c) Find a mathematical expression for P[S20 = 8|S;5 = 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 Sis = 4). (e) Now suppose that you start out with $5 (So = 5), but that cach time you play the game costs you $1. What is the probability that you still have money after playing the game 8 times (S, > 0)?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![* Y 46 ul 40% Ô 5:11 PM
Vo))
LTE1
(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 S, be the total amount
that you win after n games. Assume So = 0.
(a) Find E[S15], Var[S,5], and C,(15, 20) = Cov(Sq5, Sz0).
(b) Find the probability that you win $4 in 15 games, P[S,5 = 4].
(c) Find a mathematical expression for P[S20 = 8|S;5 = 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 = 8 n S,5 = 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 (S, > 0)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7db2178c-59da-49e2-844b-9bb48db45200%2F7f9c268b-4f80-466b-a682-a36cbb65eea8%2Fxbub408_processed.jpeg&w=3840&q=75)
Transcribed Image Text:* Y 46 ul 40% Ô 5:11 PM
Vo))
LTE1
(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 S, be the total amount
that you win after n games. Assume So = 0.
(a) Find E[S15], Var[S,5], and C,(15, 20) = Cov(Sq5, Sz0).
(b) Find the probability that you win $4 in 15 games, P[S,5 = 4].
(c) Find a mathematical expression for P[S20 = 8|S;5 = 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 = 8 n S,5 = 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 (S, > 0)?
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