Econ 41 - Final Sheet (47-50)

# Econ 41 - Final Sheet (47-50) - you winning change over...

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Unformatted text preview: you winning change over time. For the i—th match, p¢(”you win”) : .6a.2 x (i— 1). What is true about the probability go that you win the last match played? Assume the outcomes of the matches are independent. 31)]; = 10/125 b) p : 11/125 0 'p = 15/125 (€31: 32/125 e) p = 40/125 47) In question 46, what is true about the probability p of the event "a third match was not played"? a) p E [0, .45) y \ - b) p 6 L45, .5) F443“; mwi‘oh he? planed-l = Pr (. L S 7’) {Sq/Til: E12332?) = We + a» 1. a e) p 2 .65 : .llo + .31: 48) 6 equals a _/‘W a) 133) {93% 124:3 E (d { .EE/ 1:115 3.1.; *- 7, v 30/ c 0 (3320 e) 720 49) In roulette the wheel has 38 slots representing 36 numbers and two zeros. Assume you are Dr. Evil and bet all the ransom money from your last deal (“one billion dollars") on a number between 1 and 36. If your number comes up, you win and your bet is multiplied by 36. If not= you lose and get 0. What is Dr. Evil’s expected gain (in billion dollars) when playing once? —1 36 . 13-436 Fwy»: l/E‘:‘Es , F1595 = 534/553 J r c)—1/38 fun .‘1 ﬁst-1) Mina) : 137/590 '3 J (1'21 19 tfwmll '— t 1 '25: . - ' ‘ \ tail/gs 35/ ~ 3’7 5 - - 17’ - ' \3 :55 28 - . 3.3 , ’ ﬂew/- 50) Assume X m Binmial{m,q) for m = 4 and q = .5. Then p'r(X : 1) falls into which interval? a) p E [0, .15) b e[.15,.2) _ 1 C 3 [ﬂuid-2,3) ,9r(2«=1)' (14le (3’ e);:i'535"55) = L: mow) ~45 ‘-‘__/ ...
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