# Question: To illustrate the proof of Theorem 4 1 consider the random

To illustrate the proof of Theorem 4.1, consider the random variable X, which takes on the values -2, -1, 0, 1, 2, and 3 with probabilities f (-2), f (-1), f (0), f (1), f (2), and f (3). If g(X) = X2, find

(a) g1, g2, g3, and g4, the four possible values of g(x);

(b) the probabilities P[g(X) = gi] for i = 1, 2, 3, 4;

(c)

And show that it equals

(a) g1, g2, g3, and g4, the four possible values of g(x);

(b) the probabilities P[g(X) = gi] for i = 1, 2, 3, 4;

(c)

And show that it equals

**View Solution:**## Answer to relevant Questions

(a) If the probability density of X is given by Find E(X), E(X2), and E(X3). (b) Use the results of part (a) to determine E( X3 + 2X2 - 3X + 1). Find µ, µ'2, and s2 for the random variable X that has the probability distribution f(x) = 12 for x = –2 and x = 2. Show that For r = 1,2,3,..., and use this formula to express µ3 and µ4 in terms of moments about the origin. Find the moment- generating function of the discrete random variable of the discrete random variable f(x) = 2(1/3)x for x = 1,2,3,… And use it to determine the values of µ'1 and µ'2. With reference to Exercise 3.74 on page 100, find cov( X, Y).Post your question