Mathematical Expectation

Question 4.53

Suppose that a grocery store purchases 5 cartons of skim milk at the wholesale price of $1.20 per carton and retails the milk at $1.65 per carton After the expiration date, the unsold milk is removed from the shelf and the grocer receives a credit from the distributor equal to 3/4 of the wholesale price. If the probability distribution of the random variable X, the number of cartons that are sold from this lot is:

x	1	2	3	4	5
f(x)	1/15	2/15	3/15	4/15	5/15

Find the Expected Profit.


Solution:

X= No. of cartoons sold from this lot
Y= Expected Profit

Y= Selling Price - Cost Price + Credit from distributor
= 1.65x-5(1.20) +(3/4)[(5-x)(1.20)]
=1.65x -6+3/4[6-1.20x]
=1.65x -6 + 4.5- 0.90x
=0.75x-1.5

E(X) = 0(1/15) + 1(2/15) + 2(2/15) + 3(3/15) + 4(4/15) + 5(5/15)
= 46/15

E(Y) = 0.75 (46/15) - 1.5 = 0.80
The expected profit is $0.80.