9. Assume the pdf of a continuous r.v. X is a even function, and its cdf is F(x). Prove that for any real number a > 0, we have a) F(-a)= 1- F(a) = 0.5 - f p(x) dx; b) P(|X|
9. Assume the pdf of a continuous r.v. X is a even function, and its cdf is F(x). Prove that for any real number a > 0, we have a) F(-a)= 1- F(a) = 0.5 - f p(x) dx; b) P(|X|
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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Transcribed Image Text:9. Assume the pdf of a continuous r.v. X is a even function, and its cdf is F(x).
Prove that for any real number a > 0, we have
a) F(-a)= 1- F(a) = 0.5 - f p(x) dx;
b) P(|X| <a) = 2F(a) — 1;
=
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