) Determine the value of C. ) Find the marginal PDF of X. -) Find the conditional PDF of Y given X = x.
) Determine the value of C. ) Find the marginal PDF of X. -) Find the conditional PDF of Y given X = x.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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![1. Random variables X and Y are uniformly distributed over region T enclosed
by a triangle displayed by the shade in the right picture. A joint PDF of
(X,Y)' up to a unknown constant C is given by
f (r, y) = C, for 0 <x < 1, and – x < y< x
y
(1) Determine the value of C.
(2) Find the marginal PDF of X.
(3) Find the conditional PDF of Y given X = r.
(4) Find E(Y|X), and V(Y|X).
(5) Find the correlation coefficient Cor(X,Y). Hint: E(Y|X) is a linear
function of X.
(6) Are X and Y independent or not? Justify your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf4d5614-e5fa-4399-aabc-c345eeef0588%2Fe9c90a9f-a52a-42be-ba55-a925c3aed463%2Fyk7ubm5_processed.png&w=3840&q=75)
Transcribed Image Text:1. Random variables X and Y are uniformly distributed over region T enclosed
by a triangle displayed by the shade in the right picture. A joint PDF of
(X,Y)' up to a unknown constant C is given by
f (r, y) = C, for 0 <x < 1, and – x < y< x
y
(1) Determine the value of C.
(2) Find the marginal PDF of X.
(3) Find the conditional PDF of Y given X = r.
(4) Find E(Y|X), and V(Y|X).
(5) Find the correlation coefficient Cor(X,Y). Hint: E(Y|X) is a linear
function of X.
(6) Are X and Y independent or not? Justify your answer.
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