Question: The factory manager in Exercise 5.43 estimates that each breakdown costs the company $500 in repairs and loss of production. If W is the number

The factory manager in Exercise 5.43 estimates that each breakdown costs the company $500 in repairs and loss of production. If W is the number of breakdowns in a day, then $500W is the cost of breakdowns for that day.

a. Refer to the probability distribution shown in Exercise 5.43 and determine the probability distribution of the random variable 500W.

b. Determine the mean daily breakdown cost, μ500W, by using your answer from part (a).

c. What is the relationship between μ500W and μW?

d. Find σ500W by using your answer from part (a).

e. What is the apparent relationship between σ500W and σW?

f. The results in parts (c) and (e) hold in general: If W is any random variable and c is a constant,

μcW = cμW and σcW = |c|σW .

Interpret these two equations in words.

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