Ex:           A Gilbert cell is an electronic circuit that produces an output voltage that is equal to the product of two input voltages. If the input voltages, X and Y, are independent and uniformly distributed on [0,3], find the mean of Z = XY.

Sol'n:      Since X and Y are independent, the mean of the product is the product of the means:

The mean of a uniform distribution is its midpoint. Thus, we have the following value for our answer: