2. The random variables X and Y have joint density p(x, y) = = {cry Jcry(1-x) if 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.4: Values Of The Trigonometric Functions
Problem 24E
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2. The random variables X and Y have joint density
cxy(1-x) if 0<x< 1,
otherwise,
-{av
0
p(x, y) =
where c is a positive constant.
(a) Find c.
0 < y < 1,
(b) Are X and Y independent?
(c) Find EY.
(d) Find Var(X).
(e) Find the density of X+Y. (Hint: find the distribution function first.)
Transcribed Image Text:2. The random variables X and Y have joint density cxy(1-x) if 0<x< 1, otherwise, -{av 0 p(x, y) = where c is a positive constant. (a) Find c. 0 < y < 1, (b) Are X and Y independent? (c) Find EY. (d) Find Var(X). (e) Find the density of X+Y. (Hint: find the distribution function first.)
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