Hello! The question is:

A random variable X maps the outcome of a pair of dice to real numbers with the rule Y(a, b) = a - b, where a and b are the outcomes of the first and the second die, respectively, upon a roll. What is its expected value E(Y)?

This is the answer for the problem:

X H O -2 -4 Y 0 -3 W N O -2 O -1 4 3 0 6 5 4 2 1 0 Y=a-b frequency P(y) yP(y) -5 1 0.028 -0.139 -4 0.056 -0.222 -3 3 0.083 -0.250 -2 4 0.111 -0.222 5 0.139 -0.139 6 0.167 0.000 0.139 0.139 4 0.111 0.222 3 0.083 0.250 4 2 0.056 0.222 5 1 0.028 0.139 36 1 0 E(y) 0