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).
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).
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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 − α(1 – 2e¯×¹)(1 – 2e¯×²)]ex1-x2
otherwise
,0 ≤ x₁,0 ≤ x₂.
i) Find the marginal distribution of X₁.
ii) Find E(X₁X₂).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e259eaf-b603-4339-915c-6828e86fd0c4%2F9864b6ff-7de9-4088-9f61-df3a94e4c396%2Fyydvuwt_processed.png&w=3840&q=75)
Transcribed Image Text:a) Suppose that, for −1 ≤ a ≤ 1, the probability density function of (X₁, X₂) is given by
f(x₁, x₂) = {11-
[1 − α(1 – 2e¯×¹)(1 – 2e¯×²)]ex1-x2
otherwise
,0 ≤ x₁,0 ≤ x₂.
i) Find the marginal distribution of X₁.
ii) Find E(X₁X₂).
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