b) Suppose that X₁ and X₂ have the joint probability density function defined as f(x₁, x2) = {Wx₁x2₁ (Wx1x2, 0≤x₁ ≤ 1, 0 ≤ x₂ ≤ 1 elsewhere Find: i) the value of w that makes f(x₁, x₂) a probability density function. ii) the joint cumulative distribution function for X₁ and X₂. ii) P (X₂ ≤ 1X₂ ≤²).

MATLAB: An Introduction with Applications
6th Edition
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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b) Suppose that X₁ and X₂ have the joint probability density function defined as
f(x₁, x₂) = {Wx1x²,
(Wx1x2, 0≤ x₁ ≤ 1, 0 ≤ x₂ ≤ 1
elsewhere
Find:
i) the value of w that makes f(x₁, x₂) a probability density function.
ii) the joint cumulative distribution function for X₁ and X₂.
iii) P (X₂ ≤ 1 X ₂ ≤²).
Transcribed Image Text:b) Suppose that X₁ and X₂ have the joint probability density function defined as f(x₁, x₂) = {Wx1x², (Wx1x2, 0≤ x₁ ≤ 1, 0 ≤ x₂ ≤ 1 elsewhere Find: i) the value of w that makes f(x₁, x₂) a probability density function. ii) the joint cumulative distribution function for X₁ and X₂. iii) P (X₂ ≤ 1 X ₂ ≤²).
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