**Exercise 4.** Given an event \( A \subset S \), define a random variable \( X \) by:\[X(s) = \begin{cases} 1 & \text{if } s \in A, \\0 & \text{if } s \notin A.\end{cases}\]We call \( X \) an indicator variable. \( X(s) \) indicates whether the input \( s \) is in \( A \) or not.(a) Write down expression for probability mass function \( f(x) \), in terms of \( P(A) \).(b) Find the expectation \( E(X) \).

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Probability

Given an event A C S, define a random variable X by: { 1 1 if s E A, A. 0 if s X(s) = =

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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