# Question: Find the moment generating function of the discrete random variable

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.

And use it to determine the values of µ'1 and µ'2.

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

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) If X and Y have the joint probability distribution f(x, y) = 14 for x = - 3 and y = - 5, x = –1 and y = –1, x = 1 and y = 1, and x = 3 and y = 5, find cov( X, Y). Express var(X + Y), var(X – Y), and cov(X + Y, X – Y) in terms of the variances and covariance of X and Y. Referring to Example 2.28 on page 48, assume that one million people are given the test for the rare disease. Find (a) The expected number of persons given the test who have the disease; (b) The expected number of persons ...With reference to Exercise 3.92 on page 107, find the mean and the variance of the random variable in question.Post your question