11. Let f(z) and F() denote, respectively, the PDF and the CDF (cumulative distribution function) of a random variable X. The conditional PDF of X given X > 2o, where zo is a fixed 1 mmber, is defined as f(r X > ro) = f(x)/[1 – F (ro)], forr> ro, and zero elsewhere. Show that, if F(ro) < 1, then f (rX> ro) is a PDF of a random variable.
11. Let f(z) and F() denote, respectively, the PDF and the CDF (cumulative distribution function) of a random variable X. The conditional PDF of X given X > 2o, where zo is a fixed 1 mmber, is defined as f(r X > ro) = f(x)/[1 – F (ro)], forr> ro, and zero elsewhere. Show that, if F(ro) < 1, then f (rX> ro) is a PDF of a random variable.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![11. Let f(z) and F() denote, respectively, the PDF and the CDF (cumulative distribution
function) of a random variable X. The conditional PDF of X given X > zo, where zo is a fixed
mumber, is defined as f(r X > ro) = f(r)/ [1 – F (ro)], for r > I9, and zero elsewhere. Show
that, if F(ro) <1, then f (r X > ro) is a PDF of a random variable.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcfc84c11-183a-46da-b1b5-5a02b552907b%2F9aa8b9bd-af43-43d1-a68e-65ee2e01f9cd%2F696u4ja_processed.jpeg&w=3840&q=75)
Transcribed Image Text:11. Let f(z) and F() denote, respectively, the PDF and the CDF (cumulative distribution
function) of a random variable X. The conditional PDF of X given X > zo, where zo is a fixed
mumber, is defined as f(r X > ro) = f(r)/ [1 – F (ro)], for r > I9, and zero elsewhere. Show
that, if F(ro) <1, then f (r X > ro) is a PDF of a random variable.
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