6. There are two boxes. In each box there are 4 cards with a different number printed on it. The four cards have been numbered as 1,2,3,4 in each box. Two cards are drawn random from each box. The random variable X represents the difference between the number on the card from box 1 minus the number on the card from box 2.
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 M and W are defined as follows:
M = X+5 and W = (1/2)X+5
c) Find E[M] and E[W].
d) Find V[M] and V[W].
e) Mary and William play a game using the cards in the above boxes. Randomly two cards are drawn, and Mary records his score using the random variable M and William uses the random variable W. They repeat this for a large number of times and compare their scores. Comment on any likely differences or similarities of their scores.