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
icon
Related questions
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).
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).
Expert Solution
steps

Step by step

Solved in 3 steps with 1 images

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL