Exercise 2.2. Let X be a (real-valued) random variable. We define the law of X Lx(B) := P(X-'(B)) = P(w E N : X (w) € B), for all (Borel) sets B E B(R), to be the distribution of X. Prove that Lx is a probability measure on B(R).
Exercise 2.2. Let X be a (real-valued) random variable. We define the law of X Lx(B) := P(X-'(B)) = P(w E N : X (w) € B), for all (Borel) sets B E B(R), to be the distribution of X. Prove that Lx is a probability measure on B(R).
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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hello, please prove
Transcribed Image Text:Exercise 2.2. Let X be a (real-valued) random variable. We define the law of X
Сx (B) :%3D P(X -1(В) — P(w € Q: X(u) € В),
for all (Borel) sets BE B(R), to be the distribution of X. Prove that Lx is a probability
measure on B(R).
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