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fall 2005 STAT 230 Test5SolutionsV1

# fall 2005 STAT 230 Test5SolutionsV1 - STAT 230 Test#5 4:30...

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STAT 230 Test # 5 Nov 22 , 2005 4 : 30 5 : 15 pm Name : I . D : UWUserid : Circle your instructor and time slot : Cutler ( 10 : 30 ) DiCesare ( 1 : 30 ) McLeish ( 12 : 30 ) Wu ( 11 : 30 ) Wu ( 1 : 30 ) 1. A “circle of friends” is formed when a group of two or more people hold hands creating a closed curve. On any given day that a circle of friends is created, each pair of hands disjoin with probability p , independently of the other pairs of hands. A person is called isolated when they are holding no hands. Example: Circle of friends with 7 people: For any given day, let X “number of isolated people in a circle created with 30 people”. X i 1, if person i is isolated 0, otherwise ,fo r i 1,. .., N . [ 2 ] (a) Calculate P X i 1 ,for i N . P X i 1 p 2 [ 3 ] (b) Find E X i and Var X i for i N . E X i P X i 1 p 2 Var X i E X i 2 E X i 2 E X i E X i 2 P X i 1 P X i 1 2 p 2 1 p 2 [ 3 ](c)Find

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fall 2005 STAT 230 Test5SolutionsV1 - STAT 230 Test#5 4:30...

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