Find the moment-generating function for a chi square random variable and use it to show that E(

Question:

Find the moment-generating function for a chi square random variable and use it to show that E(χ²_n) = n and Var(χ²_n) = 2n.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Introduction To Mathematical Statistics And Its Applications

ISBN: 9780321693945

5th Edition

Authors: Richard J. Larsen, Morris L. Marx

See More Books

Question Posted: Dec 20, 2015 03:38 AM

See More Questions

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)=()
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.
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.
Assume you are offered a lease for a car with $227 monthly payments for 36 months after a $2,540 up front (down) payment. The alternative is that you can buy the car for $31,000 and make a $3,200...
Identity fraud occurs when someone elses personal information is used to open credit card accounts, apply for a job, receive beneï¬ts, and so on. The following relative frequency bar graph...
March 4, 2009, was one of the few good days for the stock market in early 2009. The Dow Jones Industrial Average went up 149.82 points (The Wall Street Journal, March 5, 2009). The following table...
Consider a one-period choice problem with four equally likely states of the world at the end of the period. The consumer maximizes expected utility of end-of-period wealth. The current wealth must be...
Presented below are selected qualitative characteristics of accounting information. 1. Relevance 2. Neutrality 3. Verifiability 4. Timeliness 5. Faithful representation 6. Comparability 7....
Determining Start-up Capital . . Begin by Angin the loures for the volous types of expenses in the cash flow table on the following page Start your fat month in the table that folows w starting ash...
Damon Manufacturing is preparing its master budget for the first quarter of the upcoming year. The following data pertain to Damon Manufacturing's operations: Current Assets as of December 31 (prior...
For a Student t random variable Y with n degrees of freedom and any positive integer k, show that E(Y 2k ) exists if 2k < n. (Integrals of the form are finite if > 0, > 0, and > 1.) 00 1 dy (1+y")
Is it believable that the numbers 65, 30, and 55 are a random sample of size 3 from a normal distribution with = 50 and = 10? Answer the question by using a chi square distribution. [Let Zi = (Yi ...
Grimberg, Kutikov, and Cucchiara (2005) wondered whether gender biases were evident in referrals of children for poor growth. They believed that boys were more likely to be referred even when there...
6. What are the two properties used for establishing similarity of edge pixels? 7. What is edge? 8. Give the properties of the second derivative around an edge? 9. Define Gradient Operator? 10. What...
14. Define pattern. , 15. Define pattern class. 16. List the three pattern arrangements. 17. Give the decision-theoretic methods. 18. Define the training pattern and training set. 19. Define training...
1. Write short notes on image segmentation. 2. Write short notes on edge detection 3.Write Short notes on edge linking by local processing.
4. Write short notes on the applications of artificial neural networks in image processing.
What are the functions of a finance manager of a small firm?
Define elasticity. How is it measured?
After Theorem 1.5 we note that multiplying a row by 0 is not allowed because that could change a solution set. Give an example of a system with solution set S0 where after multiplying a row by 0 the...
The SAT is to be administered at a high school. In preparation, pencils have been distributed to each of the classrooms based on the room capacity. Use the information in the following table to...
Suppose X has a Poisson distribution with a mean 0.4. Determine the following probabilities: (a) P(X = 0) (b) P(X < 2) (c) P(X = 4) (d) P(X = 8)
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.
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...
What is the NPV of a project that costs $34,000 today and is expected to generate annual cash inflows of $11,000 for the next 7 years, followed by a final inflow of $14,000 in year 8. Cost of capital...
help!!! Use the above information to calculate ending inventory using FIFO for a company that uses a perpetua/inventory system
Rocky Mountain Chocolate Factory (RMCF) founder and president Frank Crail employs 220 people in 361 outlets in the United States, Canada, United Arab Emirates, Japan, South Korea and Saudi Arabia. If...

Find the moment-generating function for a chi square random variable and use it to show that E(

Question:

Step by Step Answer:

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

Introduction To Mathematical Statistics And Its Applications

Students also viewed these Statistics questions