A simple example of a random variable is the indicator of an event A, which is denotedby IA:IA(W) =={}1 if w€ A,0 otherwise.(a) Prove that two events A and B are independent if, and only if, the associated indi-cator random variables I and I are independent.(b) Show that if X = IĄ, then E[X] = P(A).

Indicator function is defined as IA(ω) =1 if ω ∈ A, 0 otherwise

Answered: A simple example 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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