Question: Find the moment-generating function for a chi square random variable and use it to show that E( 2 n ) = n and Var( 2

Find the moment-generating function for a chi square random variable and use it to show that E(χ2n) = n and Var(χ2n) = 2n.

Step by Step Solution

★★★★★

3.40 Rating (163 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Substituting n 2 and 1 2 for ... View full answer

blur-text-image
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)

Word file Icon

681-M-C-M-S (932).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Q:

Find the moment- generating function of the continuous random variable X whose probability density is given by And use it to find ' 1 , ' 2 , and 2 . l for 0x1 elsewhere f(x)=()

Q:

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 '1 and '2.

Q:

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.

Q:

Under inference based on the normal distribution/deriving the distribution of Y hat-mu/(S/radical n) 7.3.2. Find the moment-generating function for a chi square random variable and use it to show...

Q:

Let Ï(t) be a deterministic function such that Consider the process Use Ito's rule to show that this process satisfies dZ = ÏZdW. Deduce that this process is a martingale process. Use this...

Q:

A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of 9.5 vehicles per day (randomly). The mechanic crew can service an average of 13 vehicles per day...

Q:

i need help with part b and c ! i just dont understand heres the data expalin please! Part 2. (10.5 points) Identify the distribution. The main purpose of probability density function is to model a...

Q:

Suppose that Xk is a sequence of IID Gaussian random variables. Recall that the sample variance is given by (a) Show that the sample variance can be written as a quadratic form Å2 = XTBX and...

Q:

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

Q:

Math230, 2017-18: Workshop, Coursework & Quiz Questions Coursework and Quiz marks The maximum mark obtainable through the handwritten coursework is 15 for CW01CW09. Each week there are two or three...

Q:

Miracle Printers (MP) manufactures printers. Assume that MP recently paid $600,000 for a patent on a new laser printer. Although it gives legal protection for 20 years, the patent is expected to...

Q:

a)How do you graph a lag plot of a time series in r, using its first lag.Please show r code example and output b)How do you compute and plot the first 15 lags of the autocorrelation function of a...

Q:

Problem 3 : You plan to buy a car that costs \ ( \ $ 2 5 , 5 0 0 \ ) . You will make a down payment of \ ( \ $ 5 , 0 0 0 \ ) . The remainder of the car's cost will be financed over 5 years. You will...

Q:

Estimate an appropriate ARCH, GARCH, and GARCH-M models for the variable stock return considering the Standard & Poor's 500 Index (S&P500) over a period of time.

Q:

Suppose X has a Poisson distribution with a mean 0.4. Determine the following probabilities: (a) P(X = 0) (b) P(X

Q:

Suppose that the number of customers that enter a bank in an hour is a Poisson random variable, and suppose that P(X = 0) = 0.05. Determine the mean variance of X.

Q:

The number of telephone calls that arrive at a exchange is often modeled as a Poisson random variable. Assume that on the average there are 10 calls per hour. (a) What is the probability that there...

Q:

Peaceful Cruises wants to build a new cruise ship that has an initial investment of $ 4 5 0 million. It is estimated to provide an annual cash flow over the next 2 0 years of $ 5 8 million per year....

Q:

Suppose that an investor has 8 years investment horizon. The investor is considering a 15-year semi-annual coupon bond selling at par and having a coupon rate of 9%. The investor expectations are as...

Q:

0 1 You are paying an apartment for lease at $400 per month for 25 months, monthly interest rate is 12.8%. The first payment is made today. What is the value of your 25 months apartment lease today?...