Question: Verify that if T has a t distribution with v degrees of freedom, then X = T2 has an F distribution with v1 = 1

Verify that if T has a t distribution with v degrees of freedom, then X = T2 has an F distribution with v1 = 1 and v2 = v degrees of freedom.

Step by Step Solution

★★★★★

3.45 Rating (181 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

T defined as T Z Yv in T... 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

583-M-S-S-D (2067).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Q:

The usual t distribution, as derived in Section 5.3.2, is also known as a central t distribution. It can be thought of as the pdf of a random variable of the form T = n(0,1)/X2v/v, where the normal...

Q:

Based on the result of Exercise 8.24, show that if X is a random variable having a chi square distribution with v degrees of freedom and v is large, the distribution of X v / 2v can be approximated...

Q:

Use the results of Exercises 8.25 and 8.27 to show that if X has a chi-square distribution with v degrees of freedom, then for large v the distribution of 2X 2v can be approximated with the standard...

Q:

Show that if y, has a x distribution with v degrees of freedom and Y has a distribution with v degrees of freedom, then U = Y + Y has a x distribution with v + v degrees of freedom, provided that Y...

Q:

The moment generating function of the random variable X having a chi squared distribution with v degrees of freedom is Mx t 1 2t show that the mean and variance of the chi squared distribution with v...

Q:

Moment The moment-generating function of the random variable X having a chi-squared distribution with v degrees of freedom is Mx(t)=(1-21) show that the mean and variance of the chi-squared...

Q:

Use the ALEKS calculator to solve the following problems. (a) Consider a t distribution with 9 degrees of freedom. Compute P (t2 1.71 ). Round your answer to at least three X decimal places. P(t2...

Q:

Screenshots 2 and 5 include two respectively, as the graphs did not fit in one screenshot. In total, there are 10 screenshots that need solving. I DO NOT NEED ANY EXPLANATIONS! ONLY ANSWERS. As so,...

Q:

Please help me with this question. Thank you so much!!! Question 1: In reference to one-sample hypothesis tests about the mean of the population. . When the problem states a population standard...

Q:

3. The Cadet is a popular model of sport utility vehicle, known for its relatively high resale value. The bivariate data given below were taken from a sample of fteen Cadets, each bought new two...

Q:

For the situation of Review Exercise 17.8, suppose that additional data are collected as follows. Does the process appear to be in control?Explain. Number of Defective Items Sample 3 4. 2 4 3 9. 10...

Q:

Comparative financial statements of the Boeckman Company for 2006 and 2007 are as follows: Additional information: The Boeckman Company is listed on the New York Stock Exchange. It issued 1,000...

Q:

QUESTION 1 8 ( Multiple Answer Question ) Which of the following items can be reported to the Credit Rating Agencies and impact your Credit Score? A . Unpaid Parking Tickets B . Applying for an...

Q:

A portfolio contains an investors assets.

Q:

When the horse Super Saver won the 136th Kentucky Derby, a $2 bet that Super Saver would win resulted in a return of $18. a. How much net profit was made from a $2 win bet on Super Saver? b. What...

Q:

In a clinical trial of 2103 subjects treated with Nasonex, 26 reported headaches. In a control group of 1671 subjects given a placebo, 22 reported headaches. Denoting the proportion of headaches in...

Q:

In a clinical trial of 2103 subjects treated with Nasonex, 26 reported headaches. In a control group of 1671 subjects given a placebo, 22 reported headaches. Denoting the proportion of headaches in...

Q:

Tony Begay at Saguaro Funds. Tony Begay, a currency trader for Chicago-based Saguaro Funds, uses the following futures quotes, , on the British pound () to speculate on the value of the pound. a. If...

Q:

First Simple Bank pays 8.5 percent simple interest on its investment accounts. If First Complex Bank pays interest on its accounts compounded annually, what rate should the bank set if it wants to...

Q:

A friendly merger is a\ A. merger in which the target firm's management acts to deter rather than facilitate the acquisition\ B. merger transaction that is endorsed by the target firm's management,...