a) Suppose that, for −1 ≤ a ≤ 1, the probability density function of (X₁, X₂) is given byf(x₁, x₂) = {11-[1 − α(1 – 2e¯×¹)(1 – 2e¯×²)]ex1-x2otherwise,0 ≤ x₁,0 ≤ x₂.i) Find the marginal distribution of X₁.ii) Find E(X₁X₂).

Given the joint probability density function of X1,X2 as fx1,x2=1-α1-2e-x11-2e-x2ex1-x2 , 0≤x1 ,…

Answered: a) Suppose that, for −1 ≤ x ≤ 1, the…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.1: Continuous Probability Models

Problem 16E

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a) Suppose that, for −1 ≤ x ≤ 1, the probability density function of (X₁, X₂) is given by f(x₁, x₂) = {11 - ([1 − α(1 – 2e¯x¹)(1 − 2e¯x²)]ex₁-x2 otherwise ,0 ≤ x₁,0 ≤ x₂. 0, i) Find the marginal distribution of X₁. ii) Find E(X₁X₂).