A chemical system that results from a chemical reaction has two important components among others in a blend. The joint distribution describing the proportions X₁ and X₂ of these two components is given by

A chemical system that results from a chemical reaction has two important components among others in a blend. The joint distribution describing the proportions X₁ and X₂ of these two components is given by

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

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 10E

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Question

A chemical system that results from a chemical reaction has two important
components among others in a blend. The joint distribution describing the proportions
X₁ and X₂ of these two components is given by
(2,
f(x1, x₂) = 10,
0<x1 < x₂ < 1,
elsewhere.
(a) Give the marginal distribution of X₁.
(b) Give the marginal distribution of X₂.
(c) What is the probability that component propor-
tions produce the results X₁ <0.2 and X₂ > 0.5?
(d) Give the conditional distribution fx₁x₂ (112).

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Step 1: Write the given information.

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Step 2: Give the marginal distribution of X1.

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Step 3: Give the marginal distribution of X2.

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Step 4: Find the probability that component proportions produce the results X1<0.2 and X2>0.5.

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