You are told that EX 8 and Var X 4 What are the expected v

You are told that E(X) = 8 and Var (X) = 4. What are the expected values and variances of the following expressions? Y = 3X + 2 Y = 0.6X - 4 Y = X/4 Y= aX+ b, where a and b are constants How would you express these formulas verbally?

a.)

Y= 3X+2
E(3X+2) = 3E(X)+2 = 3*8+2 = 26
Var(3X+2) = (3)^2*Var(X) = 9*4 = 36

b.)

Y= 0.6X-4
E(0.6X-4) = 0.6*E(X)-4 = 0.6*8-4 = 0.8
Var(0.6X-4) = (0.6)^2*Var(X) = 0.36*4 = 1.44

c.)

Y= X/4
E((1/4)X) = (1/4)E(X) = 2

Var((1/4)X) = (1/4)^2*Var(X) = 4/16 = 1/4

You are told that E(X) = 8 and Var (X) = 4. What are the expected values and variances of the following expressions? Y = 3X + 2 Y = 0.6X - 4 Y = X/4 Y= aX+ b,

You are told that EX 8 and Var X 4 What are the expected v

Solution

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