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.

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.

What are the possible outcomes for Ayam Grocery’s total dollar amount of losses for package A and B? For each dollar amount of loss, describe under what circumstances it would occur. In other words, what has to happen in order for each dollar amount of losses to occur? Please note that this asks about total dollar amount of losses, not number of losses.

[4 points]

For each of the possible outcomes you identify in part [a], derive the probability of the outcome occurring. [2 points]

Construct [in table form] the probability distribution for total dollar amount of losses for Package A and B. [2 points]

Calculate the expected value of total dollar amount of losses. What are the units of measurement? [2 points]

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? [4 points]

What is the amount of risk faced by Ayam Grocery? What are the units of measurement? [2 points]

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.

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