# Question: Prove Theorem 4 7 Theorem 4 7 If X has the variance 2 Then var aX

Prove Theorem 4.7.

Theorem 4.7

If X has the variance σ2, Then

var(aX + b) = a2σ2

Theorem 4.7

If X has the variance σ2, Then

var(aX + b) = a2σ2

## Answer to relevant Questions

With reference to Exercise 4.8, find the variance of g(X) = 2X + 3. In exercise The extent to which a distribution is peaked or flat, also called the kurtosis of the distribution, is often measured by means of the quantity α4 = µ4/σ4 Use the formula for µ4 obtained in Exercise 4.25 to find α4 for ...If we let RX(t) = lnMX(t), show that R'X(0) = µ and R''X(0) = σ2. Also, use these results to find the mean and the variance of a random variable X having the moment- generating function MX(t) = e4(e4 – 1) With reference to Exercise 3.74 on page 100, find cov( X, Y). With reference to Example 3.22 on page 94, and part (b) of Exercise 3.78 on page 100, find the expected value of X22X3 given X1 = 1/2.Post your question