Let X be a random vector that is split into three parts, X (Y, Z, W) Suppose that X has a continuous joint distribution with p d f f (y, z, w) Let g1(y, z w) be the conditional p d f of (Y, Z) given W w, and let g2(y w) be the conditional p d f of Y given W w Prove that g2(y w) g1(y, z w) dz

Question: Let X be a random vector that is split into three parts, X = (Y, Z, W). Suppose that X has a continuous joint distribution

Let X be a random vector that is split into three parts, X = (Y, Z, W). Suppose that X has a continuous joint with p.d.f. f (y, z, w). Let g1(y, z|w) be the conditional p.d.f. of (Y, Z) given W = w, and let g2(y|w) be the conditional p.d.f. of Y given W = w. Prove that g2(y|w) = g1(y, z|w) dz.

Step by Step Solution

★★★★★

3.39 Rating (174 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Let hyw be the marginal joint pdf ... 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)

602-M-S-C-R-V (1380).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Let X be a random variable with mean and variance 2, and let X1, X2,., Xn be a random sample of a continuous random variable with cumulative distribution function F(x). Find E[F(X(n))] and E[F(X(1))].

Let X be a random variable with E(X) = μ and V (X) = σ2. Show that the function f(x) defined by

Let X be a random variable with range [1, 1] and let fX (x) be the density function of X. Find (X) and 2(X) if, for |x|

Question: Following the principles of Epidemiologic inquiry, answer the following questions regarding one health determinant in Fredericksburg county in Virginia. www.countyhealthrankings.org,...

What is the main difference between High-Low Method and Regression Analysis? A) They are the same B) Regression Analysis is used in aggressive periods, but High-Low Method is used always C) High-Low...

public class RightTriangle ( public int hypotenuse () [ private int base: return this -hypotenuse; private int height; private int hypotenuse; public void metBase (int newBans) public RightTriangle...

1.) What is the hypothetical likelihood that a considerably number will be moved on a number 3D shape? 2.) What was the test likelihood of how often a much number was really moved utilizing the...

At the point when the monetary environment takes a plunge, like the worldwide monetary emergency (GFC) of the mid 2000s or the current COVID-19, organizations should adjust. This brings about...

Let (X,Y ) be a vector of two continuous random variables, with the following joint probability density function (joint PDF), f(x,y) = { e?3y, if 0 ?x,y 1. Find the joint PDF of the variables S = X +...

A language class has only 3 students A,B and C and they independently attend the class. The probabilities of the attendance of A, B and C on a given day are 1/2, 1/3 and 3/4 respectively. Find the...

AR Realty Trust is willing to provide sale-and-leaseback financing to Meridian. AR REalty Trust is willing to purchase the property owened by Meridian for $15 million and lease the properties back to...

Thermapure s common stock has a beta of 1 . 0 9 . If the risk - free rate is 3 . 4 percent and the expected return on the market is 9 percent, what is the company s cost of equity capital?

How could a company use benchmarking and performance measurement to improve its ethical and sustainable purchasing practices?

A balanced experimental design has a sample size of n = 11 observations at each of k = 3 factor levels. The sample averages are 1 = 48.05, 2 = 44.74, and 3 = 49.11, and MSE = 4.96. (a) Calculate...

A balanced experimental design has a sample size of n = 6 observations at each of k = 6 factor levels. The sample averages are 1 = 136.3, 2 = 152.1, 3 = 125.7, 4 = 130.2, 5 = 142.3, and 6 = 128.0,...

Find the missing values in the analysis of variance table shown in Figure 11.37. What are the p-values? In Figure 11.37 Source Degrees of freedom Sum of squares Mean squares F-statistic p-value 3.02...

The Dream Corp has annual credit sales of $2 million. Current expenses for the collection department are $40,000, bad-debt losses are 1.5%, and the days sales outstanding is 32 days. The firm is...

Urgent!!! please answer quickly I will upvote MAUBANK Berhad quotes the following for the British pound and the Australian dollar: Value of a British pound () in $ Value of a British pound in...

Instructions You can complete this assignment on Excel by following the steps outlined in detail below. I have used the symbols [ ] to designate what you should enter into Excel. For example if you...