Math 206 7. (10 points) Let X be a random variable with standard normal distribution, i.e., X ~ N(0,1). Find the c.d.f. of Y = X2 and use it to show that Y has a Gamma distribution with parameters = and ẞ = 2. a= Note: Recall that I() = √√ and recall that the p.d.f. of a random variable with Gamma distribution and parameters a and ẞ is as follows. f(x) = 2-1 Bar(a) 0, otherwise
Math 206 7. (10 points) Let X be a random variable with standard normal distribution, i.e., X ~ N(0,1). Find the c.d.f. of Y = X2 and use it to show that Y has a Gamma distribution with parameters = and ẞ = 2. a= Note: Recall that I() = √√ and recall that the p.d.f. of a random variable with Gamma distribution and parameters a and ẞ is as follows. f(x) = 2-1 Bar(a) 0, otherwise
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
![Math 206
7. (10 points) Let X be a random variable with standard normal distribution, i.e., X ~ N(0,1).
Find the c.d.f. of Y = X2 and use it to show that Y has a Gamma distribution with parameters
= and ẞ = 2.
a=
Note: Recall that I() = √√ and recall that the p.d.f. of a random variable with Gamma
distribution and parameters a and ẞ is as follows.
f(x) =
2-1
Bar(a)
0,
otherwise](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faccc1367-dc5b-4b31-bd24-5eda777b1f72%2F2b155d70-1db2-4e55-87c9-56b11caa3cc5%2Fmcwx94_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Math 206
7. (10 points) Let X be a random variable with standard normal distribution, i.e., X ~ N(0,1).
Find the c.d.f. of Y = X2 and use it to show that Y has a Gamma distribution with parameters
= and ẞ = 2.
a=
Note: Recall that I() = √√ and recall that the p.d.f. of a random variable with Gamma
distribution and parameters a and ẞ is as follows.
f(x) =
2-1
Bar(a)
0,
otherwise
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