) 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
icon
Related questions
Question

Thank you

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.
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.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning