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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 > 2o, where zo is a fixed 1 mumber, is defined as f(r X > fo) f(r)/[1 - F (ro)), for r > ro, and zero elsewhere. Show that, if F(ro) < 1, then f (r X>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 mumber, is defined as f(r X > fo) f(r)/[1 - F (ro)), for r > ro, and zero elsewhere. Show that, if F(ro) < 1, then f (r X>ro) is a PDF of a random variable.

A First Course in Probability (10th Edition)
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.
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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