a. Calculate the probability that X1 is less than 0.5 and that X2 is between 0.4 and 0.7. b. Show that these random variables are independent.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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A certain process for producing an industrial chemical yields a product containing two predominant types of impurities. For a certain volume of sample from this process, let X1 denote the proportion of impurities in the sample and let X2 denote the proportion of type I impurity among all impurities found. Suppose the joint distribution of X1 and X2, after investigation of many such samples, can be adequately modeled by the following function: (see picture)

a. Calculate the probability that X1 is less than 0.5 and that X2 is between 0.4 and 0.7.

b. Show that these random variables are independent.

 

f(x1, x₂)
=
2(1 − x₁), 0≤ X1, X2 ≤ 1
09
elsewhere
Transcribed Image Text:f(x1, x₂) = 2(1 − x₁), 0≤ X1, X2 ≤ 1 09 elsewhere
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