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# Let Y1 and Y2 denote the proportions of two different types of components in a sample ISBN: 9780495110811 47

## Solution for problem 5.12 Chapter 5

Mathematical Statistics with Applications | 7th Edition

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Problem 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 f (y1, y2) = \$ 2, 0 y1 1, 0 y2 1, 0 y1 + y2 1, 0, elsewhere. (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 11 --- Means (Sampling Distribution, Confidence Intervals, Hypothesis Tests) Sampling Distribution of a Sample Mean Example 1: The Arm and Hammer Company wants to ensure that their laundry detergent actually contains 100 fluid ounces, as indicated on the label. Historical summaries from the filling process indicate the mean amount per container is 100 fluid ounces and the standard...

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##### ISBN: 9780495110811

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