Suppose we roll a pair of fair 6sided dice Let X denote the

Suppose we roll a pair of fair 6-sided dice. Let X denote the maximum (the largest) of the outcomes on the two dice. Construct the probability distribution of X and compute its expected value.

Solution

X favourable outcomes p= favourable/36 p*x 1 1 0.027777778 0.027778 2 3 0.083333333 0.166667 3 5 0.138888889 0.416667 4 7 0.194444444 0.777778 5 9 0.25 1.25 6 11 0.305555556 1.833333 Expectation= 4.472222