Let X and Y be jointly continuous random variables with joint probability density function 0 x2, otherwise 0 y2 f(z, y) (e e *), с (a) What is the value for c? (b) Find the marginal pdfs of X and Y (c) Are X and Y independent? (d) What is P(X < Y)?

Let X and Y be jointly continuous random variables with joint probability density function 0 x2, otherwise 0 y2 f(z, y) (e e *), с (a) What is the value for c? (b) Find the marginal pdfs of X and Y (c) Are X and Y independent? (d) What is P(X < Y)?

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

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 23E

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Question

Let X and Y be jointly continuous random variables with joint probability density function
0 x2,
otherwise
0 y2
f(z, y) (e e *),
с
(a) What is the value for c?
(b) Find the marginal pdfs of X and Y
(c) Are X and Y independent?
(d) What is P(X < Y)?

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