>> life contingencies problem..

For Shoestring Swim Club, with 3 possible financial states at the end of each year:


(i)  state 0 means cash of 1500. if in state 0, aggregate member charges for the nest year are set equal to operating expenses.
(ii) state 1 means cash of 500. if in state 1, aggregate member charges for the next year are set equal to operating expenses plus 1000, hoping to return the club to state 0.
(iii) state 2 means cash less than 0. if in state 2, the club bankrupt and remains in state 2.
(iv) the club is subject to 4 risk each year. these risk are independent. each of the 4 risks occurs at most once per year, but may recur in a subsequent year.
(v) 3 of the $ risk each have a cost of 1000 and a probability of occurrence 0.25 per year.
(vi) the 4th risk has a cost of 2000 and a probability of occurrence 0.10 per year.
(vii) aggregate member charges are received at the beginning of the year.
(viii) i = 0


calculate the probability that the club is in state 2 at the end of 3 years, given that it is in state 0 at time 0.

kalau aku tiba2 bagi korang soalan kat atas ni..

apa yg korg pikir..??

adakah sama mcm ape yg aku pikir..??

skip je soklan ni..

ye..

jawapan saya skip je..

buat soklan lain..

tapi..

nk taw x..??

actually..

kalau skip..

you freely loose 5 marks..

nk taw fact yg lagi hebat x..??

soklan ni gune Markov Chain..!!

yer..

stochastic processes..

dan yg lagi hebatnye..

soklan ini xde la sesusah yg anda bygkan..

yer..

ia mmg susah..

tapi bukan lagi sampai tahap maksima..

sampai berguling2 atas lantai tarik rambut sendiri sebab xdpt buat..

*mengarut..*

anda hanya perlu taw mcm mana nk cari probability of transitioning to state by state..

okay..

tadi dlm soklan ade ckp kite start from state 0 kan..??

so kita kena kira dari state 0 to state 0,1,2 berapa probability dia..

0 to 0 : Pr (no claims) = (0.75^3)*(0.9) = 0.38

0 to 1 : Pr (one $1000 claim) = 3C1*(0.75^2)(0.25)(0.9) = 0.38

0 to 2 : 1 - 0.38 - 0.38 = 0.24

why 0.75??

 read (v). 

it said that probability of occurrence = 0.25, 

but we want probability of not occurrence, which is 1-0.25 =0.75

why 0.9??

read (vi).

it said that probability of occurrence is 0.1,

and we want the opposite, 

so 1-0.1 = 0.9

therefore, we will get this matrix :

          0.38     0.38     0.24

          0.38     0.38     0.24

           0           0          1

the question ask you what is the probability that the club in state 2 at the end of 3 years, given that it is in state 0 at time 0.

therefore,

3Q(0,2) = [ 0.38  0.38  0.24 ] [ 0.38  0.38  0.24 ] [ 0.24 ]

                                                 0.38  0.38  0.24      0.24

                                                    0       0       1           1

and you will get the answer = 0.561024  #

but..

what does the long story about..??

perlu ker..??

wajib ker buat ayat panjang2 sampai aku rase mcm jawab soklan bio pulak ni..??

okay..

Mr Ravee ckp the story leads you to get the matrix..

but..

i only found a few line that is useful enough..

what about the rest..??

ape significant cash 1500 in (i), 500 in (ii), 1000 in (iv), 2000 in (v)...??

and what is is the operating expenses..??

hurm..

better study further to find it out..

argh..!!

wanna scream right now..!!

>.<"

you will find it easy when you look at the answer..

but try to do it yourself before you see the answer script..

you will lost..