Show that for a discrete uniform random variable X, if each of the values in the range of X is multiplied by the constant c, the effect is to multiply the mean of X by c and the variance of X by c2. That is, show that E (cX) = cE(X) and V (cX) = c2 V(X).

Solution:

Step 1 of 2:

The aim is to show that E(cX) = cE(X) and