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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F676c2a72-2dc6-4daa-8824-6f013a8120dd%2F79d23877-a12e-4f17-a32a-1fdd9a058b8b%2Fvpzsrr_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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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