called invesime deviation of decision ns or losses). The gre ulcomes, the vreater I he uncertainty ision maker; the smaller the variation stial outcomes, the more predictable the decision aker's gains or losses. The two discrete probability dis tributions given in the next table were developed from historical data. They describe the potential total physical *damage losses next year to the fleets of delivery trucks of two different firms. Firm A Loss Next Year Probability § 0 500 01 01 1,000 01 1,500 2,000 2,500 29 3,000 .25 3,500 4,000 .02 4.500 01 01 5,000 01 Firm B Loss Next Year 0 200 700 1.200 1,700 2.200 2,700 3.200 3,700 4.200 4,700 Probability 00 01 879948 .02 01 a. Verity that both firms have the same expected total physical damage loss h. Compute the standard deviation of each prob- ability distribution and determine which firm faces the greater risk of physical damage to its fleet next ycar,

Other

Question

called invesime

deviation of

decision

ns or losses). The gre

ulcomes, the vreater I he uncertainty

ision maker; the smaller the variation

stial outcomes, the more predictable the decision

aker's gains or losses. The two discrete probability dis

tributions given in the next table were developed from

historical data. They describe the potential total physical

*damage losses next year to the fleets of delivery trucks

of two different firms.

Firm A

Loss Next Year

Probability

§

0

500

01 1,000

01 1,500

2,000

2,500

29 3,000

.25

3,500

4,000

.02

4.500

01 5,000

01 Firm B

Loss Next Year

0

200

700

1.200 1,700

2.200 2,700

3.200 3,700

4.200 4,700

Probability

00

01 879948

.02

01 a. Verity that both firms have the same expected total

physical damage loss

h. Compute the standard deviation of each prob-

ability distribution and determine which firm faces

the greater risk of physical damage to its fleet next

ycar,

Answer

Both firms have the same expected total physical damage loss. Firm A has a standard deviation of 1,845.45 and Firm B has a standard deviation of 1,072.45, so Firm A faces the greater risk of physical damage to its fleet next year.

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The expected total physical damage loss for both firms can be calculated by multiplying the probability of each loss by the amount of the loss and then summing...