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])

b)Find the variance and standard deviation of this probability distribution.

(i.e. Find V[X] and SD[X])

The random variables A and B are defined as follows:

A = X-10 and B = [(1/2)X]-5

c)Show that E[A] and E[B].

d)Find V[A] and V[B].

e)Arnold and Brian play a game using two fair cubes. The cubes are rolled, and Arnold records his score using the random variable A and Brian uses the random variable B. They repeat this for a large number of times and compare their scores. Comment on any likely differences or similarities of their scores.