Let X and Y be independent RVs with respective PDFS fx and fy. Show that Z = Y/X has the PDF h(z) = | fx(x)fy(zx)x|dx. Deduce that T = tan-'(Y/X) is uniformly distributed on (-1/2, 7/2) if and only if 1 T(1+z?) for z eR. Verify that this holds if X and Y both have the normal distribution with mean O and non-zero variance o?.
Let X and Y be independent RVs with respective PDFS fx and fy. Show that Z = Y/X has the PDF h(z) = | fx(x)fy(zx)x|dx. Deduce that T = tan-'(Y/X) is uniformly distributed on (-1/2, 7/2) if and only if 1 T(1+z?) for z eR. Verify that this holds if X and Y both have the normal distribution with mean O and non-zero variance o?.
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
Transcribed Image Text:Let X and Y be independent RVs with respective PDFS fx and fy.
Show that Z= Y/X has the PDF
h(z) = | fx(x)fy(zx)|x|dx.
Deduce that T = tan-'(Y/X) is uniformly distributed on (–7/2, 7/2) if and only if
1
T(1+z?)
for z eR. Verify that this holds if X and Y both have the normal distribution with mean
O and non-zero variance o?.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
