winter 2006 s230_test4sol

winter 2006 s230_test4sol - STAT 230 Test #4 March 8, 2006...

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STAT 230 Test # 4 March 8 , 2006 3 : 30 4 : 15 p . m . Name : SI . D : UWUserid : Mark / 30 Circle your instructor and time slot : 1 . McLeish ( 10 : 30 ) 2 . Zhu ( 12 : 30 ) 3 . Drekic ( 1 : 30 ) [ 8 ] 1 . Proportions of individuals with three genetic types in a population are 0.2, 0.3 and 0.5 respectively. Let X 1 , X 2 , X 3 denote the frequencies of these three types in a random sample of size 50 taken from a large population. [ 2 ]( a ) What is the distribution of X 1 ? X 1 has the Bin(50, .2) distribution [ 2 b ) Calculate E X 1 2 X 2 . Use the fact that X 1 is Bin(50,0.2) and X 2 is Bin(50,0.3) E X 1 2 X 2 50 .2 2 50  .3 20 : [ 4 c ) What is the distribution of X 3 given X 1 10? P X 3 x 3 | X 1 10 P X 3 x 3 , X 1 10 P X 1 10 P X 3 x 3 , X 2 40 x 3 , X 1 10 P X 1 10 50! 10! 40 x 3 ! x 3 ! 0.2 10 0.3 40 x 3 0.5 x 3 50 10 10 0.8 40 40 x 3 5 8 x 3 3 8 40 x 3 This is the Binomial 40,5/8 distribution.
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This note was uploaded on 03/03/2010 for the course STAT 230 taught by Professor Various during the Winter '06 term at Waterloo.

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winter 2006 s230_test4sol - STAT 230 Test #4 March 8, 2006...

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