Chapter 2.1, Problem 7E

Let a random experiment be the casting of a pair of fair six-sided dice and let X equal the smaller of the outcomes if they are different and the common value if they are equal.

(a) With reasonable assumptions, find the pmf of X.

(b) Draw a probability histogram of the pmf of X.

(c) Let Y equal the range of the two outcomes (i.e., the absolute value of the difference of the largest and the smallest outcomes). Determine the pmf g(y) of Y for y= 0, 1, 2, 3. 4, 5.

(d) Draw a probability histogram for g(y).