Question

Suppose that on each play of a certain game a gambler is equally likely to win...

Suppose that on each play of a certain game a gambler is equally likely to win or to lose. Let R = Rich Rate. In the first game (n=1), if a player wins, his fortune is doubled (r= 2), and when he loses, his fortune is cut in half (r= 1/2).

a) For the second game (n = 2), R can take values r={4,1,1/4} (Why?). Let i be the number of wins in n games. What are the possible values of R(in terms of i and n)? (There is a nice formula for this answer!)

b) What is the pmf of R(in terms of i and n)? (For example, How would you calculate P(R=14) in the n games. Again, there is a nice formula for this answer.)

c) What is the mgf of R(in terms of i and n)?

4) What is E[R] for the n game?

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Given   be the number of wins in games.

a) Then

b) The number of wins has Binomial distribution. The PMF of is

Here . is not possibles since R's are positive or negative powers of 2.

c) The MGF of is

d) E[R] for the n game is

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