Question

8. If the number of students walking in front of my office follows a Poisson process with a rate parameter λ × t, is the amountof time I observe my door in minutes. [15 points 126 b8.1-If I observe 23 students in the first 20 minutes, what is the most likely value of 2 to have given rise to this observation? 8.2- As I increase the time that I observe students walking past my door, will the estimate in (8.1-) be consistent? Justifýy your answer. k i 8.3- Solve for the distribution of the time it takes for the first student to walk past my door in the afternoon. P(K26)-1-e_6 t>0 8.4- The next week, I start keeping track of the number of grad number of undergraduate students walking in front of my office door. Assume that these ups follow independent Poisson processes with rates λg and λυ, respectively. If I observe 20 students, solve for the distribution of the number of graduate students uate students and dhe two gro

Answer 1

1)
lambda^ = 23/20 = 1.15

2)
lim Var (lamda^) = lim Var(X/t) = lim lambda = lambda

since limit is constant
it is not consistent

3)
INTER-ARRIVAL    distribution follow exponential distribution
with rate lambda