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Continuous random variables X and Y have the following joint PDF: -1 ≤ x ≤ 1, 0≤ y ≤ x² In x², to, 0, otherwise. f(x, y) = Let the event A = {Y ≤ 0.36}. Find the conditional PDF (and its range) of X given A and the expected value of X given A. Please provide the solution step by step.

Continuous random variables X and Y have the following joint PDF: -1 ≤ x ≤ 1, 0≤ y ≤ x² In x², to, 0, otherwise. f(x, y) = Let the event A = {Y ≤ 0.36}. Find the conditional PDF (and its range) of X given A and the expected value of X given A. Please provide the solution step by step.

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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Continuous random variables X and Y have the following joint PDF: nx², -1 ≤ x ≤ 1, 0 ≤ y ≤ x² f(x, y) = otherwise. Let the event A = {Y ≤ 0.36}. Find the conditional PDF (and its range) of X given A and the expected value of X given A. Please provide the solution step by step.
Transcribed Image Text:Continuous random variables X and Y have the following joint PDF: nx², -1 ≤ x ≤ 1, 0 ≤ y ≤ x² f(x, y) = otherwise. Let the event A = {Y ≤ 0.36}. Find the conditional PDF (and its range) of X given A and the expected value of X given A. Please provide the solution step by step.
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