Solution manual for first course in probability

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Solution manual for first course in probability

A Solution Manual for:A First Course In Probability: Seventh Edition by Sheldon M. Ross.John L. Weatherwax*39329IntroductionAcknowledgementsSpecial th

Solution manual for first course in probability hanks to Vincent Frost and Andrew Jones for helping find and correct various typos in these solutions.Miscellaneous ProblemsThe Crazy Passenger Proble

mThe following is known as the “crazy passenger problem” anil Is stated as follows. A line of 100 airline passengers is waiting to board the plane. Th Solution manual for first course in probability

ey each hold a ticket to one of the 100 seats on that Hight. (For convenience, let's say that the À:-th passenger in line has a ticket for the seat nu

Solution manual for first course in probability

mber k.) Unfortunately, the first person in line is crazy, and will ignore the seat number on their ticket, picking a random seat to occupy. All the o

A Solution Manual for:A First Course In Probability: Seventh Edition by Sheldon M. Ross.John L. Weatherwax*39329IntroductionAcknowledgementsSpecial th

Solution manual for first course in probability o sit in, at random. What is the probability that the last (100th) person to board the plane will sit in their proper seat (#100)?If one tries to solv

e this problem with conditional probability it becomes very difficult. We begin by considering the following cases if the first passenger sits in seat Solution manual for first course in probability

number 1. then all*wax£italuni.tnit.edu1the remaining passengers will lx* in their correct seats and certainly t If he sits in the last seat #100, t

Solution manual for first course in probability

hen certainly the last passenger cannowill end up in seat #1). If he sits in any of the 98 seats between seats #1 and #100, say seat k, then all the p

A Solution Manual for:A First Course In Probability: Seventh Edition by Sheldon M. Ross.John L. Weatherwax*39329IntroductionAcknowledgementsSpecial th

Solution manual for first course in probability nters he will have as possible seating choices seat #1, one of the seats k + 1, A- 4- 2,..., 99. or seat #100. Thus the options available to this pass

enger are the same options available to the first passenger. That is if he sits in seat #1 the remaining passengers with seat labels k+1, A'+2,..., 10 Solution manual for first course in probability

0 can sit in their assigned seats and passenger #100 can sit in his seat, or he can sit in seat #100 in which case the passenger #100 is blocked, or f

Solution manual for first course in probability

inally he can sit in one of the seats between seat A' ami seat #99. The only difference is that this A:-th passenger has fewer choices for the “middle

A Solution Manual for:A First Course In Probability: Seventh Edition by Sheldon M. Ross.John L. Weatherwax*39329IntroductionAcknowledgementsSpecial th

Solution manual for first course in probability recursive structure lets generalize this problem a bit an assume that there are jV total seats (rather than just 100). Thus at each stage of placing a

A-th crazy passenger we can choose from•seat #1 and the last or jV-th passenger will then be able to sit in their assigned seat, since all intermedia Solution manual for first course in probability

te passenger’s seats are unoccupied.•seat # N and the last or A’-th passenger will be unable to sit in their assigned seat.•any seat before the jV-th

Solution manual for first course in probability

and after the A’-th. Where the A-’-th passenger’s seat is taken by a crazy passenger from the previous step. In this case there are N — 1 - (fc+l)+1 =

A Solution Manual for:A First Course In Probability: Seventh Edition by Sheldon M. Ross.John L. Weatherwax*39329IntroductionAcknowledgementsSpecial th

Solution manual for first course in probability assenger sits in his seat. From the argument above we have a recursive structure give by111P(N,1) = ±(l) + ±(0) + ±^;>(N-i,l)‘ÀẶ l-=21 I y-1Jt=2where

the first term is where the first passenger picks the first seat (where the AT will sit correctly with probability one), the second term is when the f Solution manual for first course in probability

irst passenger sits in the jV-th seat (where the Ar will sit correctly with probability zero), and the remaining terms represent the first passenger s

Solution manual for first course in probability

itting at position A:, which will then require repeating this problem with the A'-th passenger choosing among AT - k 4- 1 seats.To solve this recursio

A Solution Manual for:A First Course In Probability: Seventh Edition by Sheldon M. Ross.John L. Weatherwax*39329IntroductionAcknowledgementsSpecial th

Solution manual for first course in probability o passible arraignments of passengers (1,2) and (2,1) of which one (the first) corresponds to the second passenger sitting in his assigned seat. This

givesp(2,l) = i.If N = 3, then from the 3! = 6 possible choices for seating arraignment https://khothuvi6n.com(1.2.3) (1,3,2) (2.3,1) (2,1,3) (3,1.2) Solution manual for first course in probability

(3.2.1)Only(1,2.3) (2.1,3) (3,2,1)correspond to admissible .seating arraignments for this problem so wo SOO thatp(3.1) - ị - I. o 2If wo hypothesis th

Solution manual for first course in probability

at p(.'V, 1) — I for all A’, placing this assumption into the recursive formulation above gives... 1 1^'1 1p(Mi) : 2V^2 2'fc 2

A Solution Manual for:A First Course In Probability: Seventh Edition by Sheldon M. Ross.John L. Weatherwax*39329IntroductionAcknowledgementsSpecial th