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Homework 11 - ~ fl I(b What is the expected amount of time...

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~J October 28, 2010 Math 351 - Homework 12 Due in class on Tuesday. Before doing these problems, read the Chapter 4 summary, in particular the entries concerning geometric random variables and negative binomial random variables. You might also wish to try problems 71 band 74c on page 178 of the text for some related questions. 1. Consider a roulette wheel consisting of 38 numbers 1 through 36, 0, and double O. Suppose Smith always bets that the outcome will be one of the numbers 1 through 12. (a) What is the probability Smith has his first win on the eighth bet? L ~ K::. f)fA.U. Z<r k? ~. 7'{ e~l X ~ ffrIJe CI"¥e.r,y t~ r-y 'v,I4'j? cU-flNel€r
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Unformatted text preview: /' ~ fl' I' , . ...-(b) What is the expected amount of time to Smith's first win? I _ £(x)~ --(c) What is the probability Smith has his fourth win on the 20th bet? C.d y~ f/~ ra hI'S .t?K C(/,:". 7:{e~ y~ q ~$'q/~ //"to~: 0/ r-I/' w':r( ~ ClI"'-~ e:ve ~e,tJ ,P ~ a ~ r ~ '"'fe. J9 :. ~(/~ 2o/~ ~~;J (fl/(I-ft)'-~-: eJ{;~/(i1J/~ (d) What is the expected amount of time to Smith's fourth win? (e) What is the probability that his fourth win happens on or before the 20th bet? (Write your It;;~~,~ain ,urn, b~ donc't :a::)t~cal~c~: t~it:; yw') c"-7 ~ 7 -/ 3J'/ l.J~ , '~7 t ·;r (0;) (fJ) Y (l//-7 ~ ,(I ?r; t; · · c --r...
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