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(3) Consider two variables Y₁, Y₂ whose joint probability density func- tion is given by 3y₁ if 0 ≤ y2 ≤ y ≤ 1, f(y₁, y2) = 0 otherwise. (a) Find the marginal density fı (y₁) 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).

(3) Consider two variables Y₁, Y₂ whose joint probability density func- tion is given by 3y₁ if 0 ≤ y2 ≤ y ≤ 1, f(y₁, y2) = 0 otherwise. (a) Find the marginal density fı (y₁) 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).

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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(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).
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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