# Question: Prove the three parts of Theorem 4 10 Theorem 4 10 If a and

Prove the three parts of Theorem 4.10.

Theorem 4.10

If a and b are constants, then

1.

2.

3.

Theorem 4.10

If a and b are constants, then

1.

2.

3.

## Relevant Questions

Given the moment- generating function MX(t) = e3t+ 8t2 , find the moment- generating function of the random variable Z = 1/4 (X – 3), and use it to determine the mean and the variance of Z. If X and Y have the joint probability distribution f(–1, 0) = 0, f(–1, 1) = 14 , f(0, 0) = 16 , f(0, 1) = 0, f(1, 0) = 1 12 , and f(1, 1) = 12 , show that (a) cov(X, Y) = 0; (b) The two random variables are not ...With reference to Exercise 3.74 on page 100, find the conditional mean and the conditional variance of Y given X = 1/4. With reference to Exercise 3.96 on page 107, what is the city’s expected water consumption for any given day? With reference to Exercise 4.71, what can we assert about the amount of time it takes a person to be served at the given restaurant if we use Chebyshev’s theorem with k = 1.5? What is the corresponding probability rounded ...Post your question