Question: Let U1 and U2 be independent random variables. Suppose that U1 is X2 with v1 degrees of freedom while U = U1 + U2 is

Let U1 and U2 be independent random variables. Suppose that U1 is X2 with v1 degrees of freedom while U = U1 + U2 is chi-square with v degrees of freedom, where v > v1. Then prove that U2 is chi-square random variable with v – v1 degrees of freedom.

Step by Step Solution

★★★★★

3.35 Rating (170 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

then by the inde... View full answer

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)

610-M-S-S-D (2172).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

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, X2, . . . ,Xn be independent random variables having an unknown continuous distribution function F, and let Y1,Y2, . . . ,Ym be independent random variables having an unknown continuous...

Let X 1 and X 2 be independent random variables having the uniform density with = 0 and = 1. Referring to Figure 7.2, find expressions for the distribution function of Y = X1 + X2 for (a) y 0; (b)...

STATISTICS 251 HOMEWORK ASSIGNMENT 8 DUE FRIDAY NOV 18 Problem 1. Let U1 , U2 be independent uniform random variables on [0, 1], and write M = max(U1 , U2 ). (a) Find the conditional joint density of...

4.35. Let X1 and X2 be independent random variables that are chi-square distributed with v1 and v2 degrees of freedom, respectively, (a) Show that the moment generating function of Z X1 X2 is ,...

Let U1, U2, , U\" be independent and identically distributed normal random variables with expectation zero and unknown variance 0'2. In this problem, we suppose that the random variables U1, U2, , U"...

Please help solve this statistics problem, please provide detailed working out for the parts, thanks! Let U1, U2, , U\" be independent and identically distributed normal random variables with...

The best definition for nonparametric statistics I can think of is when data does not fit inside the normal parameters of a normal distribution, it calls for the use of this statistical method....

4 This assignment, based on the content of Unit 4 of the Study Guide, is worth 3% of your grade. We recommend that you hand it in after you complete Unit 4. You must show all of your work in order to...

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...

The Legal Environment Dimension Could repulsive odors emanating from a neighbors property constitute unreasonable interference with a property owners rights? Why or why not?

The following information relates to a company's accounts receivable: accounts receivable balance at the beginning of the year, $300,000; allowance for uncollectible accounts at the beginning of the...

What prompted Congress to grant subsidized rates for existing construction under the National Flood Insurance Act of 1 9 6 8 ? 1 . The desire to provide free insurance for all pre - 1 9 6 9 buildings...

6- 10 In this exercise, you will use database software to design a database for managing inventory for a small business. Sylvesters Bike Shop, located in San Francisco, California, sells road,...

Determine the value of c that makes fXYZ(x, y, z) = c a joint probability density function over the region x > 0, y > 0, z > 0, and x + y + z

Continuation of Exercise 5-61. Determine the following: (a) P(X

Continuation of Exercise 5-61. Determine the following: (a) Marginal distribution of X (b) Joint distribution of X and Y (c) Conditional probability distribution of X given that Y = 0.5 and Z = 0.5...

Sort two employees based on their name, department, and age using the Comparator interface.

Convert totalDays to months, weeks, and days, finding the maximum number of months, then weeks, then days. Ex: If the input is 4 0 , then the output is: Months: 1 Weeks: 1 Days: 3

question below Consider the following mctians of two random variables X and Y: (i) 2X; (ii) Y2; (iii) X + 1"; (iv) X Y; (1:) min(X,F); (vi) maX(X,I')+ b). Suppose X and Y above are jointly Gaussian...