Question

John is considering two alternative investments (A and B). The profit possibilities and their associated probabilities of occurrence are given in the table below.

	investment a		investment b
profit = x	$20	$80	$30	$40
profitability	.70	.30	.40	.60

a. which investment should john choose to get a higher expected profit

b. please calculate the variance and standard deviation for both investments. Which has a lower variance

Answer 1

a) The expected profit for each investment is computed here as:

E(X_A) = 20*0.7 + 80*0.3 = 14 + 24 = 38
E(X_B) = 30*0.4 + 40*0.6 = 12 + 24 = 36

Therefore investment A has a higher expected profit here.

b) The second moments are first computed here as:

E(X²_A) = 20²*0.7 + 80²*0.3 = 2200
E(X²_B) = 30²*0.4 + 40²*0.6 = 1320

Therefore Var(X_A) = E(X²_A) - [E(X_A)]² = 2200 - 38² = 756
Var(X_B) = E(X²_B) - [E(X_B)]² = 1320 - 36² = 24

Therefore the variance of the 2 investments here are 756 and 24 respectively.

The standard deviations are now computed here as:

Therefore 27.50 and 4.90 are the required standard deviations here.