A simple example of a random variable is the indicator of an event A, which is denoted by IA: IA(W) = {1 if we A, otherwise. (a) Prove that two events A and B are independent if, and only if, the associated indi- cator random variables IA and I are independent. (b) Show that if X = IĄ, then E[X] = P(A).
A simple example of a random variable is the indicator of an event A, which is denoted by IA: IA(W) = {1 if we A, otherwise. (a) Prove that two events A and B are independent if, and only if, the associated indi- cator random variables IA and I are independent. (b) Show that if X = IĄ, then E[X] = P(A).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 20E
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Question
![A simple example of a random variable is the indicator of an event A, which is denoted
by 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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F153bfb9c-b05e-4b91-94e3-9e151aaf7f28%2Fa1cef06a-d6e8-43e1-af94-dcc12ab2ebf5%2Fvfbc23_processed.png&w=3840&q=75)
Transcribed Image Text:A simple example of a random variable is the indicator of an event A, which is denoted
by 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).
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