Question

Suppose that busses arrive at a station with constant rate per minute. Conferences 1. Assume that one waits at the station for 5 minutes. (a) Find the probability that there are at least 2 busses within 5 minutes. (b) Find the expectation and variance of the number of busses within 5 minutes

Answer 1

1)

Let X denote the number of buses that arrive in a 5-minute interval. Then

X Poi(5)

(52)+e-5 P(X = 1) = —, = 0,1,2,3,..

a)

Required probability =

P(X > 2) = 1 - P(X = 0) – P(X = 1)

(VS+1)x-3 - I = x-(YS) – xs-3 – 1=- -I= Ys- (Y) (79)

b)

We know that if
X ~ Poilu)
, then
E(X) = H, Var(x) = x

So,

E(X) = 54, Var(X) = 54