(a) Let X1 and X2 be independent n(0,1) random variables. Find the pdf of (X1 - X2)2/2....

Question:

(a) Let X1 and X2 be independent n(0,1) random variables. Find the pdf of (X1 - X2)2/2.
(b) If Xi, i = 1, 2, are independent gamma(ai, 1) random variables, find the marginal distributions of X1/(X1 + X2) and X2/(X1 + X2).

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

Step by Step Answer:

Related Book For book-img-for-question

Statistical Inference

ISBN: 978-0534243128

2nd edition

Authors: George Casella, Roger L. Berger

See More Books

Question Posted: May 26, 2016 05:18 AM

See More Questions

Let X1 and X2 be independent random variables and let Y1 = Ф1(X1) and Y2 = Ф2(X2). (a) Show that (b) Using (a), show that P (Y1 = r, Y2 = s) = P (Y1 = r) P (Y2 = s) so that Y1 and Y2 are...
Let X 1 and X 2 be independent random variables each having the probability distribution show that the random variables Y 1 and Y 2 are independent when Y 1 = X 1 + X 2 and Y 2 ? X 1 (X +X 2 ). x>0....
Let X1 and X2 be independent chi-square random variables with r1 and r2 degrees of freedom, respectively. Let Y1 = (X1/r1)/(X2/r2) and Y2 = X2. (a) Find the joint pdf of Y1 and Y2. (b) Determine the...
Detail how the respond to the following scenarios, with one agreeing or acknowledging the critic, and one seeking more information: "You are so lazy" {Husband says to his wife when she refuses to get...
Preston Company signs a five-year capital lease with Starbuck Company for office equipment. The annual lease payment is $10,000, and the interest rate is 10%. Required 1. Compute the present value of...
Omega Companys accountants have just completed the income statement and balance sheet for the year and have provided the following information (dollars in thousands): Other Data: The company issued...
Given the following information, calculate the cost to consumers, the benefit to producers, the change in government revenue, and the deadweight costs of a proposed 10 percent tariff on personal...
A Venture Capitalist presents Arbuckle, Inc., the shoes manufacturer with the following term sheet for a series A funding round: Amount $5 million Security Convertible Preferred Mandatory on IPO >...
Future research considerations on change management should "include individual- and group-level variables and organizational-level variables as a comparative study, across private- and public-sector...
The energy required to increase the speed of a certain car from 18 m/s to 24 m/s is 190 kJ. (a) What is the mass of the car? (b) At what speed is the car's kinetic energy equal to 190 kJ?
Given that g(x) > 0 has the property that show that is a pdf. , v > 0
X1 and X2 are independent n(0, Ï2) random variables. (a) Find the joint distribution of Y1 and Y2, where (b) Show that Yi and Y2 are independent, and interpret this result geometrically. - 3 +...
Foz Co. is considering four investment proposals (A, B, C, and D). The following table provides data concerning each of these investments: Solve for the missing information pertaining to each...
Ethics and Human ResourcesInstructions Analyze the following situation: Mrs. Rosado, general manager of Rosado & Asociados, is facing a financial dilemma. She must decide whether to fire 25% of the...
Consider the following graph and assume edges are evaluated in the same order as in prior problems. 7 U F 3 G O W6 3. 3 n 2 2 B 2 E H (1) If Prim's algorithm starts from B, what will be the second...
The states is FLORIDA Research the court-connected ADR program in effect in the federal district that serves your area and provide the following information: What forms of ADR are used in this court...
During the course of your examination of the financial statements of XYZ Corporation for the year ended December 31, 2016, you found a new account, "Investments." Your examination revealed that...
3. own a property development firm. You consider investing in three development projects, each of which will take 1.5 years, or six quarters, to complete. For each project, each quarter marks a...
Payments of $500 originally scheduled to be paid today and $300 originally scheduled to be paid three months from today are to be replaced with a single payment six months from today. Calculate the...
Cleaning Service Company's Trial Balance on December 31, 2020 is as follows: Account name Debit Credit Cash 700 Supplies Pre-paid insurance Pre-paid office rent Equipment Accumulated depreciation -...
A news organization wants to estimate the wait times to vote in the current election. A reporter asked a random sample of 19 voters how long their wait time was and found their mean wait time to be...
It has been established that the average time it takes for students to complete a bachelor's degree is approximately 4.8 years. In order to help students graduate earlier, a university wants to...
Historically, the average age to get married (for the first time) has been 29 years old. A researcher was interested in whether millennials tend to get married later than did generations of the past....
Find the future value and interest earned if $8904.56 is invested for 7 years at 5% compounded (a) semiannually and (b) continuously. (a) The future value when interest is compounded semiannually is...
A consultant advises that a fund pays out $100,000 at the end of 5 years. Provided $12,000 is invested in the fund at the start of each year, beginning immediately and continuing up to and including...
Durco Automotive needs a $2 million balance in its contingency fund 3 years from now. The chief financial officer (CFO) wants to know how much to deposit now into Durco's high-yield investment...

(a) Let X1 and X2 be independent n(0,1) random variables. Find the pdf of (X1 - X2)2/2....

Question:

Step by Step Answer:

a Since X 1 X 2 2 n0 1 X 1 X 2 2 2 X 2 1 see Example 21...View the full answer

Statistical Inference

Students also viewed these Statistics questions