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Unformatted text preview: ). In a ﬁvegame playo± series between equally matched teams, the number of games played is a r.v., N , with pmf p N ( n ) = ( ± n1 2 )± 1 2 ) n1 , n = 3 , 4 , 5 , otherwise. Find the expected number of saves this relief pitcher will make in this series. 1 Question 5: (3 marks). If X and Y are r.v.’s with equal variances, ﬁnd Cov( X + Y,XY ). Question 6: (6 marks). Let X , Y , and Z be uncorrelated r.v.’s with variances σ 2 X , σ 2 Y , and σ 2 Z , respectively. Let U = Z + X and V = Z + Y . Find ρ U,V . Question 7: Let (X,Y) have the joint pdf f X,Y ( x,y ) = ( 8 xy, < x < y < 1 , , otherwise. (a) (7 marks). Find E ( X  Y = y ) and Var( X  Y = y ). (b) (4 marks). Find the pdf of r.v. E ( X  Y ). 2...
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 Spring '11
 peskun
 Math, Variance, Total Marks

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