On Thursday, Ayam Grocery is expecting to receive Package A containing $400 wort

Question

On Thursday, Ayam Grocery is expecting to receive Package A containing $400 worth of food. Based on his past experience with the delivery service, the manager estimates that this package has a chance of 20% being lost in shipment.

1. On Friday, Ayam Grocery expects Package B to be delivered. Package B contains $600 worth of food. This package has a 25% chance of being lost in shipment.

The manager has calculated the variance for the total dollar amount of losses to be 93100. Since you want to be sure you are using correct numbers in your evaluation, prove that the manager calculated the correct variance for total dollar amount of losses. What are the units of measurement?

Explanation / Answer

There are a total of 4 possible cases:

Both A and B are lost, in which case total loss is $1000.

A is received but B is lost, in which case total loss is $600.

B is received but A is lost, in which case total loss is $400.

Both A and B are received, in which case total loss is $0.

Since delivery of A is independent of delivery of B, keeping this in mind the probability values are calculated as shown below:

Let L denote the total loss.

P(L=1000) = 0.2*0.25 = 0.05

P(L=600) = 0.8*0.25 = 0.20

P(L=400) = 0.2*0.75 = 0.15

P(L=0) = 0.8*0.75 = 0.60

The expected value of dollar amount loss is:
E(L) = 1000*0.05 + 600*0.20 + 400*0.15 + 0*0.60 = $230

Var(L) = 10002*0.05 + 6002*0.20 + 4002*0.15 + 02*0.60 - (230)2 = 93100 $2

Thus the variance has been correclty calculated. The units are dollar squared.

HOPE THIS HELPS !

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