A chemical system that results from a chemical reaction has two important components among others in a blend. The joint distribution in describing the proportions X₁ and X₂ is given to the right. (a) Give the marginal distribution fx, (x₁) of the proportion X, and verify that it is a valid density function. (b) What is the probability that proportion X₂ is less than 0.1, given that X₁ is 0.6? (a) Give the marginal distribution fx, (x1). fx, (x₁) = for 5, 5x₁₁ 3 20x2 f(x1,x2) = 20x2, 0

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I need help with this parts a and b

(a) Give the marginal distribution fx, (x₁).
fx, (x₁) =
for
0<x₂ <1
0<X1 <X2
0<x₁ <1
Transcribed Image Text:(a) Give the marginal distribution fx, (x₁). fx, (x₁) = for 0<x₂ <1 0<X1 <X2 0<x₁ <1
A chemical system that results from a chemical reaction
has two important components among others in a blend.
The joint distribution in describing the proportions X₁
and X₂ is given to the right.
(a) Give the marginal distribution fx, (x₁) of the
proportion X, and verify that it is a valid density
function.
(b) What is the probability that proportion X₂ is less than
0.1, given that X₁ is 0.6?
(a) Give the marginal distribution fx, (x1).
fx₁ (x₁) =
for
5,
3
5x₁
3
20x2
f(x1.x₂) =
3
20x2, 0<x₂<x₁ <1
elsewhere
Transcribed Image Text:A chemical system that results from a chemical reaction has two important components among others in a blend. The joint distribution in describing the proportions X₁ and X₂ is given to the right. (a) Give the marginal distribution fx, (x₁) of the proportion X, and verify that it is a valid density function. (b) What is the probability that proportion X₂ is less than 0.1, given that X₁ is 0.6? (a) Give the marginal distribution fx, (x1). fx₁ (x₁) = for 5, 3 5x₁ 3 20x2 f(x1.x₂) = 3 20x2, 0<x₂<x₁ <1 elsewhere
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