Two continuous random variables Y₁ and Y₂ has the joint density function y2, if y₁>0, y2 > 0, y₁ + y2 { otherwise. f(y1, y2) - 0, a) Find P(Y₁ > 1/2|Y₂ < 1/4). c) Find P(Y₁ > 0.5|Y₂ = 0.5). e) Find the conditional pdf f(y2|y1). < 2: b) Find the marginal pdf and CDF of Y₁. d) Are Y₁ and Y2 independent? Verify your answer. f) Find Cov(Y₁, Y₂).
Two continuous random variables Y₁ and Y₂ has the joint density function y2, if y₁>0, y2 > 0, y₁ + y2 { otherwise. f(y1, y2) - 0, a) Find P(Y₁ > 1/2|Y₂ < 1/4). c) Find P(Y₁ > 0.5|Y₂ = 0.5). e) Find the conditional pdf f(y2|y1). < 2: b) Find the marginal pdf and CDF of Y₁. d) Are Y₁ and Y2 independent? Verify your answer. f) Find Cov(Y₁, Y₂).
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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Transcribed Image Text:Two continuous random variables Y₁ and Y₂ has the joint density function
Y2, if y₁ > 0, y2 > 0, Y1+Y2 < 2;
0,
otherwise.
a) Find P(Y₁ > 1/2|Y₂ < 1/4).
c) Find P(Y₁ > 0.5|Y₂ = 0.5).
e) Find the conditional pdf f(y2|Y₁).
f(y1, y2)
-
Find the marginal pdf and CDF of Y₁.
d) Are Y₁ and Y2 independent? Verify your answer.
f) Find Cov(Y₁, Y2).
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