Assume that individuals show up at a bus station as per a Poisson cycle vvith rate A. The

transport leaves at time t. Allow X to indicate the aggregate sum ot holding up season of every one of the individuals who get on the

transport at time t. We need to decide var(X). Let N(t) signify the quantity of appearances by time t.

(a) What is

(b) Argue that

(c) What is

Assume that individuals show up at a bus station as per a Poisson interaction vvith rate A. The

transport withdraws at time t. Allow X to indicate the aggregate sum ot holding up season of every one of the individuals who get on the

transport at time t. We need to decide var(X). Let N(t) indicate the quantity of appearances by time t.

(a) What is

(b) Argue that

(c) What is

Q34

Policyholders ot a specific insurance agency have mishaps on occasion appropriated by a

Poisson measure witn rate A. The measure of time from when the mishap happens until a case is

made has circulation G.

(a) Find the likelihood there are actually n brought about yet at this point unrepoed claims at time t.

(b) Suppose that each guarantee sum nas dispersion F, and that the case sum is free

ofthe time that it takes to report the case. Track down the normal worth ot the amount of all caused yet

at this point unreported cases at time t.

Q35

For the limitless worker line with Poisson arnvals and general help circulation G, find the

likelihood that

(a) the main client to show up is additionally quick to withdraw.

Let S(t) equivalent the amount of the leftover assistance seasons of all clients in the framework at time t.

(b) Argue that S(t) is a compound Poisson irregular variable.

(c) Find

(d) Find

Q36

A streetcar begins otfvvith n riders. The occasions between progressive stops of the vehicle are

free remarkable arbitrary factors witn rate A. At each stop one rider gets off. This takes

no time, and no extra riders get on. After a rider gets off the vehicle the person in question heads back home.

Autonomously of all else, the walk takes an outstanding time witn rate u.

(a) What is the dissemination of the time at which the last rider withdraws the vehicle?

(b) Suppose the last rider withdraws the vehicle at time t. What is the likelihood that the wide range of various riders

are home around then?