Bulbs. The distributor in Exercise 5.43 estimates that each defective bulb costs him $5 for replacement. If X is the number of defective bulbs in a box, then $5 X is the cost of defective bulbs in a box.

a. Refer to the probability distribution shown in Exercise 5.43 and determine the probability distribution of the random variable 5X.

b. Determine the mean daily breakdown cost, μ5X , by using your answer from part (a).

c. What is the relationship between μ5X and μX ? (Note: From Exercise 5.43, we get μX .)

d. Find σ5X by using your answer from part (a).

e. What is the apparent relationship between σ5X and σX ? (Note:

From Exercise 5.43, we get σW .)

f. The results in parts

(c) and

(e) hold in general: If X is any random variable and c is a constant,

μcX = cμX and σcX = |c|σX .

Interpret these two equations in words.