Homework Help is Here – Start Your Trial Now!
Math
Probability
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 Για) βα xa-1e-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 Για) βα xa-1e-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. =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
See similar textbooks
icon
Related questions
Question

Kindly answer part b

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
steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
SEE MORE TEXTBOOKS