exam3-smpl-f99 - Sample Problems for Exam 3 STA 4321...

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STA 4321 Sample Problems for Exam 3 Fall 1999 Mathematical Statistics I These questions are only meant as a study aid and to help you test your knowledge. Being able to solve them does not guarantee that you are well-prepared for the exam. 1. For each of the following joint densities, indicate whether Y 1 and Y 2 are independent (Yes or No). No explanation is required. (a) f ( y 1 ,y 2 ) = ± 2 , 0 y 1 1 , 0 y 2 1 , 0 y 1 + y 2 1 , 0 , elsewhere. (b) f ( y 1 ,y 2 ) = ± e - ( y 1 + y 2 ) , y 1 0 ,y 2 0 , 0 , elsewhere. (c) f ( y 1 ,y 2 ) = ± y 1 + y 2 , 0 y 1 1 , 0 y 2 1 , 0 , elsewhere. (d) f ( y 1 ,y 2 ) = ± e - y 1 , y 1 0 , 0 y 2 1 , 0 , elsewhere. (e) f ( y 1 ,y 2 ) = ± e - y 1 , 0 y 2 y 1 < , 0 , elsewhere. 2. Let Y 1 and Y 2 denote the proportion of time, out of one workday, that employees I and II, respectively, actually spend performing their assigned tasks. The joint relative frequency behavior of Y 1 and Y 2 is modeled by the density function f ( y 1 ,y 2 ) = ± y 1 + y 2 , 0 y 1 1;0 y 2 1 0 , elsewhere. (a) Find P ( Y 1 1 2 ,Y 2 1 2 ) . (b) Find the marginal density function for Y 2 . (c) Find P ( Y 2 1 2 ) . (d) Find
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exam3-smpl-f99 - Sample Problems for Exam 3 STA 4321...

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