1. The voters in a given town arrive at the place of voting according to a...

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1. The voters in a given town arrive at the place of voting according to a Poisson process of rate λ = 100 voters per hour. The voters independently X vote for candidate A and candidate B each with probability 1/2. Assume that the voting starts at time 0 and continues indefinitely. . Conditional on 1000 voters arriving during the first 10 hours of voting, find the probability that candidate A receives n of those votes. • Again conditional on 1000 voters during the first 10 hours, find the probability that candidate A receives n votes in the first 4 hours of voting. Let S₁ be the time of the arrival of the first voter voting for candidate A. Find the density function of of S₁. • Find the probability mass function of the number of voters for candi- date B who arrive before the first voter for A. 1. The voters in a given town arrive at the place of voting according to a Poisson process of rate λ = 100 voters per hour. The voters independently X vote for candidate A and candidate B each with probability 1/2. Assume that the voting starts at time 0 and continues indefinitely. . Conditional on 1000 voters arriving during the first 10 hours of voting, find the probability that candidate A receives n of those votes. • Again conditional on 1000 voters during the first 10 hours, find the probability that candidate A receives n votes in the first 4 hours of voting. Let S₁ be the time of the arrival of the first voter voting for candidate A. Find the density function of of S₁. • Find the probability mass function of the number of voters for candi- date B who arrive before the first voter for A.

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