Suppose that a person plays a game in which he draws a ball from a box...

Suppose that a person plays a game in which he draws a ball from a box of 10 balls numbered 0 through 9. He then puts the ball back and continue to draw a ball (with replacement) until he draws another number which is equal or higher than the first draw. Let X denote the number drawn in the first draw and Y denote the number of subsequent draws needed.

(a) Find the conditional probability distribution of Y given X = x, for x = 0, 1, · · · , 9.
(b) Find the joint probability distribution of X and Y , P(X = x, Y = y).
(c) Find the probability distribution of Y , P(Y = y).
(d) Find E(Y ).

Solutions

Expert Solution

a) The conditional probability distribution of Y given X = x, for x = 0, 1, · · · , 9 is

b)Here .

The joint distribution is

c) The marginal PMF of is

A closed form expression cannot be obtained for .

d)The expecte value of is

Let , then

orchestra answered 11 months ago

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