a U XYZ b R XYZ 3 c T 2SolutionAssume that X Y and Z are

a) U = X+Y+Z

b) R = (X+Y+Z) / 3

c) T = 2

Solution

Assume that X, Y, and Z are independent random variables and that each of the random variables have a mean of 1. Further, assume x = 1, y = 2, and z = 3. Find the mean and standard deviation of the following random variables:

Mean of U = E(U) = E(X)+E(Y)+E(Z)= 1+1+1=3

SD OF U = SD(X)+SD(Y)+SD(Z)= 1+2+3=6

Mean of R = E(R) = 1/3(E(X+Y+Z) =1/3(1+1+1)=3/3 =1

SD OF R = 1/3(SD(X)+SD(Y)+SD(Z)) = 1/3(1+2+3)=6/3 =2