Review-Questions

Review-Questions - ARE 210 Review Questions page 1 1. You...

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ARE 210 Review Questions page 1 1. You are given n observations from a random sample of an experiment on the random variables X and Y , 123 ,,,, n xxx x " n yyy y " The sample means and variances for X and Y , and the sample covariance between X and Y are 1 1 n i n i x x = = , 1 1 n i n i yy = = , 1 22 1 () n xi n i sx x = =− , 1 1 n yi n i sy y = , 1 1 n xy i i n i x y y = = −⋅ − . The sum of these two variables, , 1,2,3,. .., iii zxy i n = += , is of main interest in the ex- periment. Define the sample mean for the ' i zs , 1 1 n i n i zz = = . a. Prove that =+ . Define the sample variance for the ' i , 1 1 n zi n i sz z = . b. Prove that 222 2 x y sss s =++ . c. Prove that ( ) () EZ EX EY . d. Prove that ( ) 1 ( ) () 2 (,) 2 xy x y n VZ VX VY C o vXY + = σ + σ + σ e. Prove that if X and Y are independent, then (,)0 Cov X Y = . f. Is the converse to this true? Why or why not? If your answer is yes, prove it. If your answer is no, provide a counterexample.
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ARE 210 Review Questions page 2 2. An experiment has sample space S , an algebra of subsets of the sample space σ ( S ) = F
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This note was uploaded on 08/01/2008 for the course ARE 210 taught by Professor Lafrance during the Fall '07 term at Berkeley.

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Review-Questions - ARE 210 Review Questions page 1 1. You...

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