Question

Name: 1. Suppose you have the following probability distribution. Calculate the mean, variance, standard deviation, and coefficient of variation. State of Nature Profit Level Probability of Occurrence 500 0.3 Optimistic Most Likely Pessimistic 100 0.6 -400 0.10

Answer 1

Part A:

Expected Ret = Sum [ Ret ] / n

Scenario	Prob	Profit	Prob * Ret
Optimistic	0.300	500.00	150.00
Most Likely	0.600	100.00	60.00
Pessimistic	0.100	-400.00	-40.00
Expected Ret	170.00

Option D is correct.

Part B:

SD = SQRT [ [ Sum[ Prob * ( X-AvgX)^2 ) ] ] ]

State	Prob	Profit	(X-AvgX)	(X-AvgX)^2	Prob * (X-Avg X)^2
Boom	0.3000	500.00	330.00	1,08,900.00	32,670.00
Normal	0.6000	100.00	-70.00	4,900.00	2,940.00
Recision	0.1000	-100.00	-270.00	72,900.00	7,290.00
Sum[ Prob * ( X-AvgX)^2 ) ]	42,900.00
SD = SQRT [ [ Sum[ Prob * ( X-AvgX)^2 ) ] ] ]	207.12

Option E

Part C:

Coefficient of Variation = SD / Mean
It specifies risk each unit of return
Particulars	Amount
Standard Deviation	207.12
Mean	170.00

Coefficient of Variation = SD / Mean

= 207.12 / 170.00

= 1.22

OPtion E

Part D:

State	Prob	Profit	(X-AvgX)	(X-AvgX)^2	Prob * (X-Avg X)^2
Boom	0.3000	500.00	330.00	1,08,900.00	32,670.00
Normal	0.6000	100.00	-70.00	4,900.00	2,940.00
Recision	0.1000	-100.00	-270.00	72,900.00	7,290.00
Variance = Sum[ Prob * ( X-AvgX)^2 ) ]	42,900.00

OPtion E is correct.

Pls do rate, if the answer is correct and comment, if any further assistance is required.