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

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Chapter1: Combinatorial Analysis
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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).
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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