ABSTRACT
Exercise 3.1. Consider two urns (denoted Urn 1 and Urn 2). Urn 1 contains 2 white balls and 1 black ball; Urn 2 contains 1 white ball and 2 black balls.
Suppose that one ball is randomly drawn from Urn 1 and is put into Urn 2; then, balls are selected one-at-a-time without replacement from Urn 2 until a white ball is obtained. Let Y denote the number of balls selected from Urn 2 until a white ball is obtained (e.g., if the first ball selected from Urn 2 is black and the second one is white, then Y = 2). Provide a formula, not a table, for the probability distribution pY (y) of the random variable Y , and then use this formula to find numerical values for E(Y ) and V(Y ).
