A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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![**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 \( E(X) \).](https://content.bartleby.com/qna-images/question/b47fe1c9-1465-464b-a626-f1fe4168d136/4bb7a12d-58a4-4051-9100-e1d03e7fe4c2/p0kc3ll_processed.png)
Transcribed Image Text:**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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It is given that the random variable X is an indicator variable and X(s) indicates whether the input s is in A or not.
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