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With A, B, X defined as before, determine whether the following statements are true or false: 1. A and B are independent. True False 2. A and B are conditionally independent, given X = 0.

With A, B, X defined as before, determine whether the following statements are true or false: 1. A and B are independent. True False 2. A and B are conditionally independent, given X = 0.

A First Course in Probability (10th Edition)
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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True or False With A, B, X defined as before, determine whether the following statements are true or false: 1. A and B are independent. True False 2. A and B are conditionally independent, given X = 0. True False 3. A and B are conditionally independent, given X = 1. True False
Transcribed Image Text:True or False With A, B, X defined as before, determine whether the following statements are true or false: 1. A and B are independent. True False 2. A and B are conditionally independent, given X = 0. True False 3. A and B are conditionally independent, given X = 1. True False
Expectation Let X, Y, Z be independent discrete random variables with and 2. Find Var (B). Var (B) E[X] =2 Let A = X(Y+Z) and B = XY. 1. Find E [B]. E[B]= E [X²] = 20 3. Find Var (B|X = 2). Var (B|X= 2) = 4. Find E [AB]. E [AB] = E[Y] =0 E[Z]=0, E [Y²] = E [Z²] = 16, Var (X) = Var (Y) = Var (Z) = 16.
Transcribed Image Text:Expectation Let X, Y, Z be independent discrete random variables with and 2. Find Var (B). Var (B) E[X] =2 Let A = X(Y+Z) and B = XY. 1. Find E [B]. E[B]= E [X²] = 20 3. Find Var (B|X = 2). Var (B|X= 2) = 4. Find E [AB]. E [AB] = E[Y] =0 E[Z]=0, E [Y²] = E [Z²] = 16, Var (X) = Var (Y) = Var (Z) = 16.
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