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In Exercise 5.12, we were given the following joint probability density
For the two chemicals under consideration, an important quantity is the total proportion Y1 + Y2 found in any sample. Find E(Y1 + Y2) and V(Y1 + Y2).
5.12 Let Y1 and Y2 denote the proportions of two different types of components in a sample from a mixture of chemicals used as an insecticide. Suppose that Y1 and Y2 have the joint density function given by
(Notice that Y1 + Y2 ≤ 1 because the random variables denote proportions within the same sample.) Find
- a P(Y1 ≤ 3/4, Y2 ≤ 3/4).
- b P(Y1 ≤ 1/2, Y2 ≤ 1/2).
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Chapter 5 Solutions
Mathematical Statistics with Applications
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill