Question

A financial broker has calculated the expected values of two different financial instruments X and Y....

A financial broker has calculated the expected values of two different financial instruments X and Y. Given E(X) = 186 E(Y) = 136 SD(X) = 48 and SD(Y) = 42 a.) Find E(0.5X-0.2Y+5) b.) Find SD(0.5X-0.2Y+5)

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Answer #1

Given : E(X)=186, E(Y)=136

SD(X)=48, SD(Y)=42

Var(X)= 2304, Var(Y)=1764

a) we have to find E(0.5X-0.2Y+5)

Use property,E(aX+bY) = aE(X)+bE(Y)

E(0.5X-0.2Y+5) = 0.5 *E(X) - 0.2 E(Y)

by putting given values,we get

E(0.5X-0.2Y+5) = 0.5*186 - 0.2*136

= 93 - 27.2

= 65.8

Ans : E(0.5X-0.2Y+5) = 65.8

b) We have to find SD(0.5X-0.2Y+5)

we know that,

also we know property, Var(aX + bY) =a2Var(X)+b2Var(Y) and Var(constant) =constant

Therefore, we find Var (0.5X+0.2Y+5) = (0.5)2*var(X) - (0.2)2*var(Y) + var(5)

= 0.25*2304 - 0.04*1764 + 5

= 576 - 70.56 + 5

Var (0.5X+0.2Y+5) = 510.44

  

  

Ans : SD(0.5X-0.2Y+5) = 22.59

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