a) Suppose that, for -1 ≤ a ≤ 1, the probability density function of (X₁, X₂) is given byƒ (x₁, x₂) = {[1— a(1S[1 − α(1 — 2e¯×¹)(1-2e-*²)]*¹*2otherwise,0 ≤ x₁,0 ≤ x₂.i) Find the marginal distribution of X₁.ii) Find E(X,X₂).

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(1-2e¹)(1-2e-*²)]*¹*2 ,0≤x₁,0 ≤ x₂. otherwise i) Find the marginal distribution of X₁. ii) Find E(X,X₂).

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