2. Suppose that two teams play a series of games that ends when one of them has won 2 games. Suppose that each game played is, independently, won by team A with probability p. Let X be the number of games played. (a) Find the pmf for X. All probabilities should be in terms of p. (b) Find the expected number of games that are played. E[X] will be in terms of p. (c) Show that this number is maximized when p = 1/2. Hint: consider local extrema of g(p) = E[X].
2. Suppose that two teams play a series of games that ends when one of them has won 2 games. Suppose
that each game played is, independently, won by team A with
games played.
(a) Find the pmf for X. All probabilities should be in terms of p.
(b) Find the expected number of games that are played. E[X] will be in terms of p.
(c) Show that this number is maximized when p = 1/2. Hint: consider local extrema of
g(p) = E[X].
Be very detailed with your algebra.
Given information:
Suppose that two teams play a series of games that ends when one of them has won 2 games.
Suppose that each game played is, independently, won by team A with probability p.
Let X be the number of games played.
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