a) Suppose that, for -1 < a < 1, the probability density function of (X₁, X₂) is given byf(x₁, x₂) = {11-a(1-([1-a(1-2e-x¹)(1-2e-*²)]e*¹*₂otherwise,0 ≤ x1,0 ≤ x₂.i) Find the marginal distribution of X₁.ii) Find E(X₂X₂).

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) = {1- [[1-a(1-2e-¹)(1-2e-*)]*₁-* ,0 ≤ x1,0 ≤ x₂. otherwise i) Find the marginal distribution of X₁. ii) Find E(X₂X₂).

a) Suppose that, for-1 ≤ a ≤ 1, the probability density function of (X₁, X₂) is given by f(x₁, x₂) = {1- [[1-a(1-2e-¹)(1-2e-)]₁-* ,0 ≤ x1,0 ≤ x₂. otherwise i) Find the marginal distribution of X₁. ii) Find E(X₂X₂).