2. If three random variables have the joint density (r + y)e-, for 0 0 10. f(r, y, z) = elsewhere (a) find the probability that X 1; (b) check whether the three random variables are independent; (c) check whether any two of the three random variables are pairwise independent.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 20E
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2.
If three random variables have the joint density
S{(r + y)e-, for 0 <r < 1, 0 < y< 2, z > 0
10,
f(x, y, 2) =
elsewhere
(a) find the probability that X <Y and Z > 1;
(b) check whether the three random variables are independent%3;
(c) check whether any two of the three random variables are pairwise independent.
Transcribed Image Text:2. If three random variables have the joint density S{(r + y)e-, for 0 <r < 1, 0 < y< 2, z > 0 10, f(x, y, 2) = elsewhere (a) find the probability that X <Y and Z > 1; (b) check whether the three random variables are independent%3; (c) check whether any two of the three random variables are pairwise independent.
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