a) Suppose that, for -1 < a < 1, the probability density function of (X₁, X₂) is given byf(x₁, x₂) = {11 - α(1 - 2e-x¹)(1 – 2e˜×²)]e*¹¬×²-,0 ≤ x₁,0 ≤ x₂.0,otherwisei) Find the marginal distribution of X₁.ii) Find E(X₁X₂).

Answered: a) 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 16E

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

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