You and a friend, along with an eccentric rich probabilist, are observing a Poisson process whose...

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You and a friend, along with an eccentric rich probabilist, areobserving a Poisson process whose arrival rate is Î» = .5 per hour.The probabilist offers to pay you $100 if there is at least onearrival between noon and 2pm, and also offers to pay your friend$100 if there is at least one arrival between 1pm and 3pm.
a. What is the probability that either you or your friend, orboth, gets $100?
b. What is the probability that one of you wins $100, but notboth?
Consider a Poisson process with arrival rate Î» per minute. Giventhat there were three arrivals in the first 2 minutes, find theprobability that there were k arrivals in the first minute; do thisfor k = 0, 1, 2, and 3.
Given that P(A) = .4, P(A âˆ© B) = .1, and P((A âˆª B) c ) = .2,find P(B).

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4.5 Ratings (947 Votes)

aPthat in 2 hours at least one arrivalPX11PX01e0520520006321hence P both gets 100Pfm noon to 2 pm one customer arrivesand from 1pm to 3pm at least one customer arrives063210632103996bprobability that See Answer

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