Voters for candidate A and candidate B arrive at a polling station as per a Poisson process with equal probability. The rate of arrival of voters is 100 voters perhour. Therefore, you can assume that the arrival of voters for candidate A and ofvoters for candidate B are two independent Poisson processes, each having a rate50 voters per hour. If 1000 voters arrive in 10 hours, compute the probability that m of them are for candidate A. Hint: Use indpendence of the two processes. b) Compute the probability that in the first 4 hours, candidate A has m votes, given again that the total voters arriving in 10 hours are 1000. Hint: Use conditiong, Bayes theorem and the above result in the first part on sum of two Poisson processes.

Question

Voters for candidate A and candidate B arrive at a polling station as per a Poisson process  with  equal  probability.   The  rate  of  arrival  of  voters  is  100  voters  perhour.  Therefore, you can assume that the arrival of voters for candidate A and ofvoters for candidate B are two independent Poisson processes, each having a rate50 voters per hour.  If 1000 voters arrive in 10 hours,  compute the probability that m of them are for candidate A. Hint:  Use indpendence of the two processes. b)  Compute the probability that in the first 4 hours, candidate A has m votes, given again that the total voters arriving in 10 hours are 1000.  Hint:  Use conditiong, Bayes  theorem  and  the  above  result  in  the  first  part  on  sum  of  two  Poisson processes.