For a Student t random variable Y with n degrees of freedom and any positive integer k,

Question:

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 α > 0, β > 0, and αβ > 1.)

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

Show that as n, the pdf of a Student t random variable with n df converges to f Z (z). (To show that the constant term in the pdf for T n converges to 1/2, use Stirlings formula, n! .= 2n n n e n )...
For the random variable Y with pdf fY (y) = 2/3 + 2/3 y, 0 y 1, find P (3/4 Y 1).
Police cars are randomly stationed throughout the town. When an emergency occurs, the distance a police car must travel north or south is a random variable X with density fX(x) = 1/6 for 0 x 6, and...
Ice Cool produces two different models of air conditioners. The activities, costs, and cost drivers associated with the production processes follow. Process Assembly Finishing Support Activity...
In a poll conducted July 2729, 2010, a random sample of 2163 adults (aged 18 and over) was asked, When you see an ad emphasizing that a product is Made in America, are you more likely to buy it, less...
Develop an analysis of inflation by including the following: Choose a product or service you currently consume/use, such as apparel or educational services, that is included in the CPI's "market...
Explain induced drag and how the pilot changes it during flight.
Hudson Co. reports the contribution margin income statement for 2015 below. Using this information, compute Hudson Co.s (1) Break-even point in units (2) Break-even point in sales dollars. HUDSON co....
Describe the principal advantages of alternative dispute resolution. While a mediated settlement is not binding on the parties, it brings with it certain benefits. What are they? What are the...
According to a Pew Research Center nationwide telephone survey of American adults conducted by phone between March 15 and April 24, 2011, 25% of American college graduates said that their student...
Evaluate the integral using the Student t distribution. 1424 dx 1+x2
Find the moment-generating function for a chi square random variable and use it to show that E( 2 n ) = n and Var( 2 n ) = 2n.
What is the relationship between managements financial statement assertions and audit evidence?
Unicorn Inc. is an Australian listed firm that pays corporate tax rate of 30%. Unicorn recently conducted an off-market share buyback under tax determination TD2004/22. On 10th March 2022, Unicorn...
How do inclusive leaders champion diversity, equity, and inclusion initiatives within organizational ecosystems, dismantling systemic barriers, amplifying marginalized voices, and fostering a culture...
Dru Lindsay drove his car 12,842 miles last year. The total of variable costs was $3,822.54 and of fixed costs was $2,174.00. What was the cost per mile to operate his car last year? Round to the...
Why Study OM? It allows firms to enjoy ? by allowing firms to compete more ?
Crane Bucket Co . , a manufacturer of rain barrels, had the following data for 2 0 2 4 : Sales quantity: 2 , 340 barrels Unit selling price: $ 5 0 per barrel Unit variable costs: $53 per barrel Fixed...
Use Table 10.1 to find the sum of each series. 1 - 3x2 2! + 34x4 4! 36x6 6! +.
Two mutually exclusive investment alternatives are being considered. Alternative A requires an initial investment of $20,000 in a machine. Annual operating and maintenance costs are anticipated to be...
Continuation of Exercises 3-86 and 3-87. (a) Calculate the finite population corrections for Exercises 3-86 and 3-87. For which exercise should the binomial approximation to the distribution of X be...
Use the binomial approximation to the hypergeometric distribution to approximate the probabilities in Exercise 3-92. What is the finite population correction in this exercise?
Suppose X has a Poisson distribution with a mean 4. Determine the following probabilities: (a) P(X = 0) (b) P(X < 2) (c) P(X = 4) (d) P(X = 8)
Discuss the cultural differences between China and the United States. What would be the biggest adjustments I might need to make if working there as an expatriate? What are the most...
In her Ted talk, Kristi Rogers talks about the future of advertising and why it's crucial for ads to be relevant. She points out that even though we have lots of data and technology for digital ads,...
Consider ways in which an employer can make an employee feel like part of the team and/or empower them to act. More specifically, please respond to the following questions: How can an employer work...

For a Student t random variable Y with n degrees of freedom and any positive integer k,

Question:

00 1 dy (1+y")

Step by Step Answer:

Let T be a Student t random variable with n degrees of freedom Then Where C is the prod...View the full answer

Introduction To Mathematical Statistics And Its Applications

Students also viewed these Statistics questions