HW26Answers(10.1)

HW26Answers(10.1) - Math331 Spring 2008 Instructor David Anderson Section 10.1 Homework Answers Homework pgs 412 414's 3 5 11 13 3 We have that V

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Math331, Spring 2008 Instructor: David Anderson Section 10.1 Homework Answers Homework: pgs. 412 - 414, #’s 3, 5, 11, 13. 3. We have that V ar ( X ) = V ar ( Y ) = V ar ( Z ) = 1 and E [ X ] = E [ Y ] = E [ Z ] = 0, therefore, E [ X 2 ] = E [ Y 2 ] = E [ Z 2 ] = 1. Using this and independence gives E [ X 2 ( Y + 5 Z ) 2 ] = E [ X 2 ( Y 2 + 10 Y Z + 25 Z 2 )] = E [ X 2 Y 2 ] + 10 E [ X 2 Y Z ] + 25 E [ X 2 Z 2 ] = E [ X 2 ] E [ Y 2 ] + 10 E [ X 2 ] E [ Y ] E [ Z ] + 25 E [ X 2 ] E [ Z 2 ] = 1 1 + 10 1 0 0 + 25 1 1 = 26 . 5. Let X be the number of cereal boxes the customer must open until all Fve prizes are found. Let X 1 be the number of cereal boxes needed to be opened before the customer Fnds the Frst unique prize, X 2 be the number of cereal boxes needed to be opened after the customer Fnds the Frst prize and until he/she Fnds a second unique prize, X 3 be the number of cereal boxes needed to be opened after the customer Fnds the second unique prize and until he/she Fnds a third unique prize, etc. for
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This note was uploaded on 06/24/2008 for the course MATH 331 taught by Professor Anderson during the Spring '08 term at Wisconsin.

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HW26Answers(10.1) - Math331 Spring 2008 Instructor David Anderson Section 10.1 Homework Answers Homework pgs 412 414's 3 5 11 13 3 We have that V

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