a) Suppose that, for -1 ≤ a ≤ 1, the probability density function of (X₁, X₂) is given byf(x₁,x₂) = {11₁-([1-a(1-2e-x₁)(1 - 2e-*₂)]e*₁-*z ,0 ≤ x₁,0 ≤ x₂.otherwisei) Find the marginal distribution of X₁.ii) Find E(X₁X₂).

Answered: Suppose that, for -1 ≤ a ≤ 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 25E

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

Suppose that, for -1 ≤ a ≤ 1, the probability density function of (X₁, X₂) is given by f(x₁, x₂) = {11,- [1-a(1-2e-¹)(1-2e-²)]e₁-² ,0 ≤ x₁,0 ≤ x₂- otherwise i) Find the marginal distribution of X₁. ii) Find E(X₁X₂).