In x², f(x, y) = ») - 0, -1 ≤x≤1, 0≤ y ≤ x² otherwise. Let the event A = {Y ≤ 0.36}. Find the conditional PDF (and the range) of Y given A and the expected value of Y given A. Please provide the solution step by step.
In x², f(x, y) = ») - 0, -1 ≤x≤1, 0≤ y ≤ x² otherwise. Let the event A = {Y ≤ 0.36}. Find the conditional PDF (and the range) of Y given A and the expected value of Y given A. Please provide the solution step by step.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 1CR
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Question
![Continuous random variables X and Y have the following joint PDF:
In x²,
f(x, y)
-1 ≤ x ≤ 1,0 ≤ y ≤ x²
otherwise.
Let the event A = {Y ≤ 0.36}.
Find the conditional PDF (and the range) of Y given A and the expected
value of Y given A. Please provide the solution step by step.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03946f05-98e1-403c-8105-d8cfe5413137%2Fe2343569-2340-44bc-8eb0-c3925d9670cc%2Fsbw015_processed.png&w=3840&q=75)
Transcribed Image Text:Continuous random variables X and Y have the following joint PDF:
In x²,
f(x, y)
-1 ≤ x ≤ 1,0 ≤ y ≤ x²
otherwise.
Let the event A = {Y ≤ 0.36}.
Find the conditional PDF (and the range) of Y given A and the expected
value of Y given A. Please provide the solution step by step.
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