1.Becky is playing a board game. She throws two fair, 6-faced dice with the numbers 1-6 on them, and the sum will determine how many spaces she will move. (a) Let X be the number of spaces that she will move. Find the expected value E(X). (b) Find the variance V (X). 2. Becky is playing a board game in which she glides along a path continuously instead of jumping from one space to another. She uses a random number generator to get two numbers from the continuous uniform distribution on [1,6], and the sum will determine how far she will move. (a) Let X be the distance that she will move. Find the expected value E(X). (b) Find the variance V (X). (Hint: The uniform distribution is on [1,6], not [0,6]. Think about the implications.)

When doing this homework, you may find the following identities useful: n K = n(n + 1) 2 k=1 n K2 = n(n + 1)(2n + 1) k=1 6