To compete with Netflix, the owner of a local movie rental store decides to try

Question

To compete with Netflix, the owner of a local movie rental store decides to try sending DVDs through the mail. To plan for this endeavor, she sends DVDs to her friends to obtain data on delivery times when DVDs are mailed to customers and return times when DVDs are mailed back to the store.

Let the random variable X denote the delivery time when a DVD is mailed to a customer, and let the random variable Y denote the return time when a customer mails the DVD back to the store.

The store owner found that the mean delivery time, E(X), was 1.9 days, and that the standard deviation of delivery time, SD(X), is 0.5 days. She found that the mean return time, E(Y), is 2.9 days, with a standard deviation SD(Y) of 0.7 days.

Question 1. Determine the mean and standard deviation of the total transit time for a DVD (that is, the delivery time when mailed to the customer plus the return time when mailed back to the store).

_______ days, mean total transit time

_______ days, standard deviation of total transit time (use 3 decimal places)

Question 2. On average the return time Y is greater than the delivery time X. Determine the mean and standard deviation of how much the return time Y exceeds the delivery time X.

_______ days, mean of how much the return time exceeds the delivery time.

_______ days, standard deviation of how much the return time exceeds the delivery time.

Explanation / Answer

Q1.

E(X+Y) = E(X) + E(Y) = 1.9 + 2.9 = 4.8 days

V(X+Y) = V(X) + V(Y) + 2 Cov(X,Y) = 0.5*0.5 + 0.7*0.7 + 0 = 0.74

SD(X+Y) = ?V(X+Y) = ?0.74 = 0.86 days

Q2.

E(Y-X) = E(Y) - E(X) = 2.9 - 1.9 = 1 day

V(Y-X) = V(Y) + V(X) - 2 Cov(X,Y) = 0.7*0.7 + 0.5*0.5 - 0 = 0.74

SD(Y-X) = ?V(Y-X) = ?0.74 = 0.86 days

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