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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?

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)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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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