(3) Consider two variables Y₁, Y₂ whose joint probability density func- tion is given by f(y₁, y2) = [3y₁ if 0 ≤ y2 ≤ y ≤ 1, 0 otherwise. (a) Find the marginal density fı (y₁) of Y₁. (b) Compute the conditional probability P(Y₂ 2 1/2|Y₁ = 3/4). (c) Compute E(Y2), E(Y2) and E(Y₁Y₂). (d) Compute the covariance Cov(Y₁, Y2).
(3) Consider two variables Y₁, Y₂ whose joint probability density func- tion is given by f(y₁, y2) = [3y₁ if 0 ≤ y2 ≤ y ≤ 1, 0 otherwise. (a) Find the marginal density fı (y₁) of Y₁. (b) Compute the conditional probability P(Y₂ 2 1/2|Y₁ = 3/4). (c) Compute E(Y2), E(Y2) and E(Y₁Y₂). (d) Compute the covariance Cov(Y₁, Y2).
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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:(3) Consider two variables Y₁, Y₂ whose joint probability density func-
tion is given by
f(y1, y2)
=
[3y₁ if 0 ≤ y2 ≤ Y₁ ≤ 1,
0
otherwise.
(a) Find the marginal density f₁(₁) of Y₁.
(b) Compute the conditional probability P(Y2 ≥ 1/2|Y₁ = 3/4).
(c) Compute E(Y2), E(Y2) and E(Y₁Y₂).
(d) Compute the covariance Cov(Y₁, Y2).
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