09 - BTRY/STSCI 4080 Homework # 9 Due Date: 11/18/10...

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BTRY/STSCI 4080 Homework # 9 Due Date: 11/18/10 Problem numbers beginning with P (e.g., P1) denote problems from the “PROB- LEMS” section; those beginning with T (e.g., T1) denote problems taken from the “THEORETICAL EXERCISES” section. 1. In an isoceles triangle, two sides are of equal length λ> 0 , and the length of the other side is determined by the angle between them, say A . Suppose that the angle A is a continuous random variable with pdf equal to f ( a )= ka ( π - a ) I (0 <a< π 2 ) , where k> 0. Let Y denote the total area of the isoceles triangle; that is, Y = 1 2 λ 2 sin A . (a) Determine k and Fnd pdf of Y . (b) ±ind E( Y ) and Var( Y ). Hint: in (b), you will need to be able integrate functions of theform a x (sin a ) y for certain integer values of x and y ;youmayneedtoreturntothesect ionontr ignometr icintegrals in your calculus book . 2. The only three categories in a quality control scheme for classifying items produced in a certain factory are “acceptable”, “minor defect”, or “major defect”. A particular carton

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This note was uploaded on 11/29/2010 for the course STSCI 4080 taught by Professor Strawderman during the Fall '10 term at Cornell.

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09 - BTRY/STSCI 4080 Homework # 9 Due Date: 11/18/10...

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