As in an earlier exercise, busy people leave the park according to a Poisson process with rate λ1=3/hour. Relaxed people leave the park according to an independent Poisson process with rate λ2=2/hour. Each person, upon leaving the park, makes a decision whether to enter the nearby coffee shop. Each busy person decides to enter the coffee shop with probability 1/4. Each relaxed person decides to enter the coffee shop with probability 1/2. The decisions of different persons are independent, and also independent from all other aspects of the Poisson processes that define this model. Assume that no other people enter the coffee shop. Is the process of arrivals at the coffee shop (people entering the coffee shop) a Poisson process? If yes, enter below its rate. If not, enter 0.
7/4
a) 5
b) 2
ignore the previous post
thanks
a) e^(-0.5)
b) 3/2*e^(-3/2)
can one help me in this question
There are n people in line, indexed by i=1,…,n , to enter a theater with n seats one by one. However, the first person ( i=1 ) in the line is drunk. This person has lost her ticket and decides to take a random seat instead of her assigned seat. That is, the drunk person decides to take any one of the seats 1 to n with equal probability. Every other person i=2,…,n that enters afterwards is sober and will take his assigned seat (seat i ) unless his seat i is already taken, in which case he will take a random seat chosen uniformly from the remaining seats.
Suppose that n=3 . What is the probability that person 2 takes seat 2?
(Enter a fraction or a decimal accurate to at least 3 decimal places.)
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