A and B are two competing companies An investor decides whet

A and B are two competing companies. An investor decides whether to buy 100 shares of A. or 100 shares of B, or 50 shares of A and 50 shares of B.

E(X)= 2*.5 + (-2)*.5 = 0 and E(X²)=4*.5+4*.5=4

V(X)=4-0=4

E(Y)=4*0.2+ (-1)*0.8 = 0 and E(Y²)=16*0.2+1*0.8=4

V(Y)=4-0=4

Let a nd b respectively denote the no.of shares of A nad B respectively.

Then total profit in this scheme is aX+bY.

E(aX+bY)=aE(X)+bE(Y) = 0

and V(aX+bY)=a²V(X)+b²V(Y) = 4(a²+b²)

(a)

Here a=100,b=0

expected profit=0 and variance=4(100²) = 400000

(b)

Here a=0,b=100

expected profit=0 and variance=4(100²) = 400000

(c)

Here a=50,b=50

expected profit=0 and variance=4(50²+50²)=20000