2. Let X be a Chi-squared random variable with density function a fx (x) = exp x > 0. Suppose Y is independent of, and has the same distribution as, X. (a) Let Z = vX. Show that the density function of Z is given by %3D fz(z) = 2a exp z > 0. Hence state the value of a. (b) Let V = X +Y and W = X/Y. Show that the joint density of V and W is given by 1 fv,w(v, w) = v, w > 0. ev/2 2T /w(w +1)
2. Let X be a Chi-squared random variable with density function a fx (x) = exp x > 0. Suppose Y is independent of, and has the same distribution as, X. (a) Let Z = vX. Show that the density function of Z is given by %3D fz(z) = 2a exp z > 0. Hence state the value of a. (b) Let V = X +Y and W = X/Y. Show that the joint density of V and W is given by 1 fv,w(v, w) = v, w > 0. ev/2 2T /w(w +1)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![2. Let X be a Chi-squared random variable with density function
a
fx (x) =
exp
x > 0.
Suppose Y is independent of, and has the same distribution as, X.
(a) Let Z = vX. Show that the density function of Z is given by
%3D
fz(z) = 2a exp
z > 0.
Hence state the value of a.
(b) Let V = X +Y and W = X/Y. Show that the joint density of V and W is
given by
1
fv,w(v, w) =
v, w > 0.
ev/2
2T /w(w +1)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F222d3f55-cd8b-4f6c-864b-1ec0693b4d87%2F2c614b45-5a54-4c5d-a3a0-9f7c719916fd%2Fkis0gw9_processed.png&w=3840&q=75)
Transcribed Image Text:2. Let X be a Chi-squared random variable with density function
a
fx (x) =
exp
x > 0.
Suppose Y is independent of, and has the same distribution as, X.
(a) Let Z = vX. Show that the density function of Z is given by
%3D
fz(z) = 2a exp
z > 0.
Hence state the value of a.
(b) Let V = X +Y and W = X/Y. Show that the joint density of V and W is
given by
1
fv,w(v, w) =
v, w > 0.
ev/2
2T /w(w +1)
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