Suppose that X and Y have joint density given by: f (x, y) = 15x²y, 0 < x < y < 1. (a) Find the marginal pdf of Y. (b) Find the conditional pdf of X given Y. (c) Find the conditional expectation of X given Y = 1/3.

Suppose that X and Y have joint density given by: f (x, y) = 15x²y, 0 < x < y < 1. (a) Find the marginal pdf of Y. (b) Find the conditional pdf of X given Y. (c) Find the conditional expectation of X given Y = 1/3.

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.

Chapter9: Multivariable Calculus

Section9.1: Functions Of Several Variables

Problem 34E: The following table provides values of the function f(x,y). However, because of potential; errors in...

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Question

#2,
Suppose that X and Y have joint density given by:
f (x, y) = 15x²y,
0 < x < y < 1.
(a) Find the marginal pdf of Y.
(b) Find the conditional pdf of X given Y.
(c) Find the conditional expectation of X given Y = 1/3.
(d) Are X andY independent? Show this in two different ways.
(e) Give an integral expression for P(X + 2Y < 1), but do not evaluate it.

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