Question

1.    Two fair cubes are rolled. The random variable X represents the difference between the values of the two cubes.

 

a)    Find the mean of this probability distribution. (i.e. Find E[X])

Answer 1

Let X1 denote the value of the first cube and X2 denote the value of the second. Then, due to the linearity of expectation E[X] = E[X1 - X2] = E[X1] + E[-X2] = E[X1] - E[X2] = 0, as X1 and X2 have the same distributions.