X and Y are jointly continuous with joint pdf f(x, y) = {0₁ 10, cxy if 0≤x, 0≤y, x + y ≤ 1 otherwise. (a) Find c. (b) Find P(Y>X) (c) Find marginal pdf's of X and of Y (d) Are X and Y independent?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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X and Y are jointly continuous with joint pdf
cxy
f(x, y) = {Ct
if 0≤x, 0≤y, x + y ≤ 1
otherwise.
(a) Find c.
(b) Find P(Y>X)
(c) Find marginal pdf's of X and of Y
(d) Are X and Y independent?
Given:
We start (as always!) by drawing the support set. (See below, left.)
support set
Hints for (a):
Range of y is from 0 to 1 - x
Range of x is from 0 to 1
y=1-x
0.5
y=x
Blue: subse
of support s
with y>x
1 X
Hints for (b):
Range of y is from x to 1 - x
Range of x is from 0 to 0.5
Transcribed Image Text:X and Y are jointly continuous with joint pdf cxy f(x, y) = {Ct if 0≤x, 0≤y, x + y ≤ 1 otherwise. (a) Find c. (b) Find P(Y>X) (c) Find marginal pdf's of X and of Y (d) Are X and Y independent? Given: We start (as always!) by drawing the support set. (See below, left.) support set Hints for (a): Range of y is from 0 to 1 - x Range of x is from 0 to 1 y=1-x 0.5 y=x Blue: subse of support s with y>x 1 X Hints for (b): Range of y is from x to 1 - x Range of x is from 0 to 0.5
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