3. If the continuous random vector (X, Y) with conditional density function Y given X = x is f(x)=2e-0¹-*), x 2|X = 1) (c) E[X] and E[X|Y=y].
3. If the continuous random vector (X, Y) with conditional density function Y given X = x is f(x)=2e-0¹-*), x 2|X = 1) (c) E[X] and E[X|Y=y].
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![3. If the continuous random vector (X, Y) with conditional density function Y given X = x
is f(x)=2e-0¹-*), x < y<∞ and 0<x<∞, and zero elsewhere, and marginal
density function of X is f(x) = he¯^*, 0<x<∞, and zero elsewhere.
Find the
(a) joint density function of (X, Y).
(b) P(Y>2|X = 1)
(c) E[X] and E[X|Y=y].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F60abd4de-ba2d-4a53-b8fc-e1d2e0799cec%2Fc592b1b8-47a7-49bb-94da-f43b5f90d421%2Frlct8sb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. If the continuous random vector (X, Y) with conditional density function Y given X = x
is f(x)=2e-0¹-*), x < y<∞ and 0<x<∞, and zero elsewhere, and marginal
density function of X is f(x) = he¯^*, 0<x<∞, and zero elsewhere.
Find the
(a) joint density function of (X, Y).
(b) P(Y>2|X = 1)
(c) E[X] and E[X|Y=y].
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