Quiz_8_Sol - Q uiz 8 Name: _ October 30, 2009 During a...

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Quiz 8 Name: ___________________________ October 30, 2009 During a meteor shower, an average of 2 shooting stars can be seen in 10 minutes. Let S be the number of stars you see in a 10 minute period. 1. State the distribution and parameters of S. S~Poisson( =2) λ 2. If you stand outside for 10 minutes, what is the probability you see at least 2 shooting stars? P(S 2) = 1-P(S<2) = 1 – [P(S=0)+P(S=1)] = 1 – [ - !+ - ! e 2200 e 2211 ] = .59 3. You and a friend are both watching the meteor shower and see stars independently of each other. What is the probability that you both see at least 2 shooting stars? .59^2 = .35 ~ ( ) X Poisson λ ~ , X Binomialn p ~ , , X HypergeometricN n p = = - ! PX x e λλxx ( = )= ( - )( - ) P X x nxpx 1 p n x ( = )= ( - ) - P X x NpxN 1 p n xNn = EX λ = EX np = EX np = VarX λ = ( - ) VarX np 1 p = - - ( - ) VarX N nN 1np 1 p
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~ ( ) X Poisson λ ~ , X Binomialn p ~ , , X HypergeometricN n p = = - ! PX x e λλxx ( = )= ( - )( - ) P X x nxpx 1 p n x ( = )= ( - ) - P X x NpxN 1 p n xNn = EX λ = EX np = EX np = VarX λ = ( - ) VarX np 1 p = - - ( - ) VarX N nN 1np 1 p
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This note was uploaded on 03/27/2012 for the course STAT 225 taught by Professor Martin during the Fall '08 term at Purdue University-West Lafayette.

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Quiz_8_Sol - Q uiz 8 Name: _ October 30, 2009 During a...

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