The joint density of X and Y is given by f(x, y) = C(y – x)e, -y < x < y, 0 < y < ∞ (a) Find C. (b) Find the density function of X. (c) Find the density function of Y . (d) Find P(|X| < Y /2)

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.6: Proportion And Variation
Problem 22E: Find the constant of proportionality. z is directly proportional to the sum of x and y. If x=2 and...
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The joint density of X and Y is given by
f(x, y) = C(y –- x)e, -y < x < y, 0 < y < ∞
(a) Find C.
(b) Find the density function of X.
(c) Find the density function of Y .
(d) Find P(|X] < Y /2)
Transcribed Image Text:The joint density of X and Y is given by f(x, y) = C(y –- x)e, -y < x < y, 0 < y < ∞ (a) Find C. (b) Find the density function of X. (c) Find the density function of Y . (d) Find P(|X] < Y /2)
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