Homework Help is Here – Start Your Trial Now!
Math
Statistics
Given T Gam(2, 0) with shape 2 and scale 0 >0 - measured in years. Let Z = XT for some constant > > 0. In addition, given Y > 0, which follows a Y~ Gam(2, n) with shape 2 and scale n >0 and PQ is defined as PQ = Z - Y. Assuming Y Z and that random variable X, with the Gam(a, scale = B) density is 1 I(a) Ba xa-1 e-x/B a, ß > 0 f(x, a, B) for x > 0 and f(x; a, B) = 0 elsewhere. a. Find the density of the transformation Z = XT, fz(z). b. What is the joint density fzy (z, y)? Show that it is a valid density. =

Given T Gam(2, 0) with shape 2 and scale 0 >0 - measured in years. Let Z = XT for some constant > > 0. In addition, given Y > 0, which follows a Y~ Gam(2, n) with shape 2 and scale n >0 and PQ is defined as PQ = Z - Y. Assuming Y Z and that random variable X, with the Gam(a, scale = B) density is 1 I(a) Ba xa-1 e-x/B a, ß > 0 f(x, a, B) for x > 0 and f(x; a, B) = 0 elsewhere. a. Find the density of the transformation Z = XT, fz(z). b. What is the joint density fzy (z, y)? Show that it is a valid density. =

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question

Kindly answer part c

Given T~ Gam(2, 0) with shape 2 and scale 0 >0 - measured in years. Let Z = XT for some constant > > 0. In addition, given Y > 0, which follows a Y~ Gam(2, n) with shape 2 and scale n >0 and PQ is defined as PQ = Z - Y. Assuming YI Z and that random variable X, with the Gam(a, scale = B) density is 1 I(a) Ba xa-1 e-x/B a, ß > 0 f(x, a, B) for x>0 and f(x; a, B) = 0 elsewhere. a. Find the density of the transformation Z = XT, fz(z). b. What is the joint density fzy (z, y)? Show that it is a valid density. c. Compute the probability that Pzy (PQ < 0) by double-integrating over the joint from part (b). =
Transcribed Image Text:Given T~ Gam(2, 0) with shape 2 and scale 0 >0 - measured in years. Let Z = XT for some constant > > 0. In addition, given Y > 0, which follows a Y~ Gam(2, n) with shape 2 and scale n >0 and PQ is defined as PQ = Z - Y. Assuming YI Z and that random variable X, with the Gam(a, scale = B) density is 1 I(a) Ba xa-1 e-x/B a, ß > 0 f(x, a, B) for x>0 and f(x; a, B) = 0 elsewhere. a. Find the density of the transformation Z = XT, fz(z). b. What is the joint density fzy (z, y)? Show that it is a valid density. c. Compute the probability that Pzy (PQ < 0) by double-integrating over the joint from part (b). =
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS