Question: Gamma and Dirichlet distributions. Let s 2, > 0, 2 0;1OEs and suppose that X1; : : : ; Xs are independent random

Gamma and Dirichlet distributions. Let s 2, ˛ > 0, 2 0;1OEs and suppose that X1; : : : ; Xs are independent random variables with gamma distributions ˛;.1/; : : : ; ˛;.s/.

Also, let X D Ps iD1 Xi . Show that the random vector .Xi=X/1is is independent of X and has the Dirichlet distribution D that was defined in Problem 7.28.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock 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

Students Have Also Explored These Related Probability Statistics Questions!

I will rate helpful please assist. Problem 14.47. Let {X,}nen, be a Markov chain with the transition matrix P = WIH WIH GIN WHO 1. Find all stationary distributions.Problem H.431. Let {Xheun he a...

Thank you so much. Problem 14.47. Let {X,}nen, be a Markov chain with the transition matrix P = WIH WIH GIN WHO 1. Find all stationary distributions.Problem H.431. Let {Xheun he a Markov chain whose...

I need to help in these question. Can you guys help me to solve it? Question 2 [5 points] Suppose that X1 , X2, .. .are random variables such that Xconverges to 1 in probability. Which of the...

Math 174E Fall 2016 Homework 2 (due: Fr, Oct. 7) The purpose of this homework assignment is to model the dependence of the time value Vn of a call option at the money with a given strike price as a...

AMS 311, Spring 2016 Homework 8 Due at the beginning of class, April 19, 2016 1. (20 points) Two friends A and B go on a date and agree to meet at 7pm. Friend A is an impatient person and will scold...

AMS 311, Spring 2017 Homework 8 Due at the beginning of class, April 20, 2017 1. Two friends A and B go on a date and agree to meet at 7pm. Friend A is an impatient person and will scold b if A...

Suppose X1, X2,... are independent random variables with 1 1 P{X;= -1} = 2' P{X; = 1} = | P{X; = 0} = P{X; = Let S 0 and Sn - 4 X++X. Let Fr denote the information contained in X1, ..., Xn. 1. Which...

Q9some type is wrong, can refer to the attach file. In a study of the relationship between an explanatory variable Z and a response variable Y , n independent observations are taken in the form of...

Determine if the given statements in (1)-(10) are true or false (circle your answer). 1. For independent random variables X and Y , we have that Var(X+ Y ) = Var(X) + Var(Y ). 2. Let Y = 3X1 + 2X2...

Consider the following enterprise, which includes books, authors and publishers. Authors are people with normal attributes, like name, date of birth, etc., but in addition they wrote one or more...

Two long, parallel wires separated by 0.20 m carry equal currents of 1.5 A in the same direction. Find the magnitude and direction of the magnetic field 0.15 m away from each wire on the side...

Payments from customers are due within: Multiple Choice None of the answer choices are correct. 3 0 days. 4 5 days. 6 0 days. 1 5 days.

Merck Research Labs conducted $ an experiment to evaluate the effect of a new drug using the single-T swim maze. Nineteen impregnated dam rats were captured and allocated a dosage of 12.5 milligrams...