need help

Hi, Can someone pleaseeee help me on these questions, as i really need helppppppppp.

1. An motor insurance company operates an NCD system with 3 levels
that have discounts of 0%, 30% and 60%.

• Following a claim free year a policyholder moves up one level (or
remains at level 3).

• Following a year with exactly one claim the policyholder drops
down one level (or remains at level 1).

• Following a year with two or more claims the policyholder drops
down to level 1 (or remains at level 1).

The number of claims (N) from each policyholder in a year can be
assumed to have a Poisson(lamda) distribution so that

P[N = x] = ((lamda)^xe^-(lamda))/x!


(a) Write the transition matrix, P, for this system.

(b) Find the equilibrium proportion of policyholders in each level in
terms of lamda.

(c) If 100% of policyholders are in level 1 in year 1 then find the
proportion of policyholders in each level in years 2 and 3.

(d) 10,000 good drivers (lamda = 0.1) and 10,000 bad drivers (lamda = 0.2)
all start out at level 1 in year 1. Find the expected numbers of
good and bad drivers in each level in years 2 and 3 and in the
equilibrium position.

(e) If the premium charged to a policyholder in level 1 is P (where
P is the same for good and bad drivers) then find the average
premium paid by good and bad drivers in the equilibrium position.
Comment briefly on the effectiveness of the NCD system.

(f) If all claims are for £1000 and the company charges a premium
to exactly cover the claims cost in the equilibrium position then
find P.

 

John thats the thing, i dont have the notes with me and they are too expensive to buy. i have do 1a and b but i am not sure on1c and 1d