Sloution to problem set 8

Probability and Statistics for Engineering and the Sciences (with CD-ROM and InfoTrac )

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Solutions for Homework 8 Section 5.2 22. a. E( X + Y ) = ) 02 )(. 0 0 ( ) , ( ) ( + = + ∑∑ xy y x p y x 10 . 14 ) 01 )(. 15 10 ( ... ) 06 )(. 5 0 ( = + + + + + b. E[max (X,Y)] = + y x p y x ) , ( ) max( 60 . 9 ) 01 )(. 15 ( ... ) 06 )(. 5 ( ) 02 )(. 0 ( = + + + = 23. Let h(X,Y) = # of individuals who handle the message. y h(x,y) 1 2 3 4 5 6 1 - 2 3 4 3 2 2 2 - 2 3 4 3 x 3 3 2 - 2 3 4 4 4 3 2 - 2 3 5 3 4 3 2 - 2 6 2 3 4 3 2 - Since p(x,y) = 30 1 for each possible (x,y), E[h(X,Y)] = 80 . 2 ) , ( 30 84 30 1 = = y x h 24. E(XY) = E(X) E(Y) = L L = L 2
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Sec. 5.3 Page 234: 37, 38, 39 37. P(x 1 ) .20 .50 .30 P(x 2 ) x 2 | x 1 25 40 65 .20 25 .04 .10 .06 .50 40 .10 .25 .15 .30 65 .06 .15 .09 a. x 25 32.5 40 45 52.5 65 () x p .04 .20 .25 .12 .30 .09
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Sloution to problem set 8 - Solutions for Homework 8...

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