Question: Show that the mgf of a X2 random variable is M (t) = (1 2t)v/2. Using the mgf, show that the mean and variance

Show that the mgf of a X2 random variable is M (t) = (1 – 2t)–v/2. Using the mgf, show that the mean and variance of a chi-square are v and 2v, respectively.

Step by Step Solution

★★★★★

3.28 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

If with then th... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

610-M-S-S-D (2186).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Show that the moment generating function (mgf) for the binomial distribution is m(t) = (1 + e t ) n , and use it to obtain the first two moments. Show that the mgf for the Poisson distribution is...

Find the mgf of a Bernoulli random variable with parameter p. Use this to find the mgf of a binomial random variable with parameters n and p.

A joint random variable (X1, X2) is said to have a bivariate normal distribution if its joint density is given by for (a) Show that E(X1) = Î¼X1 and E(X2) = ÏX2. (b) Show that...

Solve all. 5 Consider the success run chain in Example 8.2.16. Suppose that the chain has been running for a while and is currently in state 10. (a) What is the expected number of steps until the...

Markov chain. 8 Consider an irreducible Markov chain on a finite state space, such that the transition matrix is symmetric (pij = pji for all i, j ? S). Find the stationary distribution. 9 Markov...

Set 4 Due April 26, 2016 BENG 100 S16 1. See iPython notebook on Ted. Fill it in, run it, and make sure it works. Submit on Ted. 2. Suppose that Y is a geometric random variable of parameter p, 1 (a)...

Activity Directions: Consider a scenario in which several processes compete for access to the same resource (e.g., a file or some memory address). When a process is starved due to resource...

Exercise 1 LetX and Y be two independent Poisson random variables with distribution parameters A1 and A2, respectively. Show that the conditional distribution of X given X + Y is binomial. (Hint:...

Variance o2 = E[(X - u)?] (where u = EX ) tells you how far the distribution is spread out of from its mean. Similarly, E [(X - u)4/o'] which is called Kurtosis, tells you how heavy the tail of your...

Using the following attached reading titled "An Institutional Explanation of the Democratic Peace by Bruce Bueno de Mesquita, James D. Morrow, Randolph M. Siverson and Alastair Smith compose a paper...

The March accounting records of Jackson & Associates include these accounts: Requirement Compute Jackson & Associates net cash provided by operating activities during March. Use the indirect method....

Can a firm operating in the upward- sloping portion of its average cost curve be a natural monopoly? Explain.

Why couldn't Newton determine the value of the gravitational constant?

Do you have any foreign language proficiency?

Continuation of Exercise 5-102 (a) What is the conditional distribution of the number of calls requiring five rings or more given that eight calls are answered in two rings or less? (b) What is the...

Determine the value of c such that the function f (x, y) = cx2y for 0

Continuation of Exercise 5-104. Determine the following: (a) P(X 2, 1

Read the article from https://www.quora.com/What-is-the-difference-between-packet-firewall-stateful-firewall-and-application-firewall Explain the difference between packet firewall, stateful firewall...

I want to know what the margin of error is ? For b) Question 12 of 16 - /1 E Plastic Microfiber Pollution on Shorelines In a study, we see that plastic microparticles are contaminating the world's...

Commercial real estate Three multiple regressions, MODEL A, MODEL B, and MODEL C, were run on data from 52 commercial rental real estate properties in the San Fernando valley of Los Angeles. The...