1. Say that E(X) = 10; and var(X) = 5. Find E(Y) and var(Y) in the following cases:

a) Y = 0.37X – 3.79

b) Y = 0.37X + 5.73

c) Y = (3x^2+2)/4

d) Y = aX + b

2. Prove that:

a) E(X^2) greater than equal to [E(X)]^2 (Hint: this follows immediately from the definition of the varianceand from one of the properties of the variance).

b) cov(X, Y ) = E(XY )- , where = E(X) and = E(Y ). (Hint: Use the definition

of covariance).

Please see the attached file.

1. Say that E(X) = 10; and var(X) = 5. Find E(Y) and var(Y) in the following cases:

a) Y = 0.37X – 3.79

b) Y = 0.37X + 5.73

c) Y = (3x^2+2)/4

d) Y = aX + b

Answer

We have the result

E(aX+b) = aE(X)+b

V(aX+b) =a2V(X)

a). …

Calculation of Expected Value E(X), Variance V(x) and Covariance of random variable.