>> pirates coins distribution..

salam to all readers..

=)

when i first saw this question..

the first thing that i do is laughing.

hahahahahahaha..

such a nice way of applications.

okay.

stop laughing.

start calculating.

want to know how to calculate?

here i show you.

x ≡ 3 mod 17

x ≡ 10 mod 16

x ≡ 0 mod 15

gcd (17,16,15) = 1

therefore, a solution exist.

x = x0 mod (17)(16)(15)

x = x0 mod 4080

from x ≡ 3 mod 17  --> x = 3 + 17k

3 + 17k ≡ 10 mod 16

17k ≡ 7 mod 16

k ≡ 7 mod 16

k = 7 + 16m

x = 3 + 17( 7 + 16m)

x = 122 + 272m 

122 + 272m ≡ 0 mod 15

272m ≡ -122 mod 15

2m ≡ -2 mod 15

2m ≡ 13 mod 15

16m ≡ 104 mod 15

m ≡ 14 mod 15

m = 14 + 15n

x = 122 + 272( 14 + 15n)

x= 3930 + 4080n

therefore, the least no of coins stolen is 3930.

tak percaya? 

try substitute balik dalam equation yang dia bagi.

if there is 17 pirates, they have 3 coins left.

3930 - 17*231 = 3

if there is 16 pirates, they have 10 coins left.

3930 -16*245 = 10

if there is 15 pirates, they have no coins left.

3930 - 15*262 = 0

it makes sense, right?

happy playing with numbers!

(^_^)v

>> demotivated..

that most demotivated moment..

when you finally finished the question that the lecturer gave you..

and he review your answer thoroughly.

and then he said,

"this is not the best answer.. because i'm not sure whether the interest rate is right."

and the questions after after that..

i just do it with no heart..

T_T

>> test postpone?

salam to all readers..

=)

semalam borak-borak dengan course mate.

dorang kata test LC postpone 1/11/2012.

biar betul?

tapi lecturer tak kata apa-apa pun.

takde announcement pun..

tolong la jangan postpone test ni.

tolong la.

kenapa?

sebab yang pertama.

kalau postpone, lecturer pernah inform dia nak masukkan Multiple Decrement Model sekali..

korang tahu tak, MDL tu sangat susah?

tak boleh study seminggu je dah tahu jawab?

tahu tak?

sekurang-kurangnya kena ambil masa beberapa hari untuk faham 1 part tu je..

tu belum part-part yang lain.

gila ke apa?

sebab yang kedua.

terlalu dekat dengan test Investment.

aku tahu la korang pandai.

tapi please la be considerate sikit to average student like me.

LC is kill, when the test is just before Investment, it double kill you know!

i want to pass and graduate next year.

please........

jangan postpone test LC..

even though aku pun belum 100% prepared lagi untuk test, tp at least biar la test LC dalam minggu depan.

at least minggu depan aku cuma fokus untuk 1 test je.

and the following week i can focus on Investment.

please...

please..........

i beg you guys with all my heart..

dont postpone the LC test..

*luahan hati seorang pelajar yg tertekan*

>> internship..

salam to all readers..

=)

hadia birthday yang paling bermakna tahun ni..

dapat internship kat satu bank besar dekat dgn rumah..

oh yeah..~~

Alhamdulillah..

(^_^)v

sungguh gembira bukak email hari ni..

Alhamdulillah..

everything happen better than expected..

(^_^)v

sem 1 2011/2012

ramai orang first day kuliah hari isnin..

tapi aku first day kuliah hari selasa..

nampak macam seronok..

sebab aku takkan mengeluh lagi setiap kali tiba hari isnin seperti sebelum-sebelum ni..

tapi tahukah anda?

selasa-khamis jadual saya sangat menarik..

start pukul 8 pagi..

habis pukul 9.30 malam..

yang lagi sakit hati..

rabu kelas aku ade 2 je..

8-11am, 6.30-9.30pm

ade gap 7 jam 30 minit tu beb..!

cerita pasal first day..

macam excited je kan?

mula-mula tu memang la agak excited..

siap bagun pukul 6 pagi siap-siap tu..

almaklumlah..

dah 4 bulan lebih tak pergi kuliah..

*ke sebab kelas pukul 8? =_=" *

tapi bila dah masuk kelas..

rase macam semester ni dah start berkurun lamanya.. 

errr..

rasa macam dah lali dengan kuliah-kuliah ni sume..

macam takde apa-apa yang baru pun..

cuma bas je yang baru..

hehe..

walaupun sem ni aku amek 20 jam kredit..

tapi jadual aku tak nampak macam budak yang amik 20 jam kredit pun..

mane taknye..

lobang sana..

lobang sini..

gap between 2 classes is 2-3 hours..

except for wednesday..

i got 7 hour and half gap..!

exam?

okay la kot susunan exam aku..

seminggu 2 paper je..

xde la berat sangat..

yang paling penting..

tiada 2 paper dalam 1 hari..

cukup2 la tu..

sakit taw tak?

pesanan buat junior-junior..

kalau-kalau ada yang terbaca blog akak ni..

*akak la sgt*

susun jadual elok-elok..

yang penting jangan cari pasal amik subjek yang exam 2 paper dalam 1 hari..

boleh mati kegilaan keluar dewan peperiksaan nanti..

oh ya..

dengar-dengar khabar bangunan BP sudah dipindahkan..

ke belakang kolej 6..

tak begitu pasti..

kalau salah..

jom sama-sama kita bunuh Shahid..!

hahahahaahhahahahaha...

=_="

>> congak..

macam mana korg kira ni?

 28 x 7 = ?

3.5 x 9 = ?

tekan calculator?

itu semestinya..

tapi kalau kalkulator xde..

mcm mane?

macam mana cara korang congak?

adekah korang menggunakan sifir 7 kali 28?

dan sifir 9 kali dengan 3.5?

atau korg pikir mcm aku?

cara aku pikir cmne pulak?

ha..

cmni :

28 paling dekat dengan 30..

so 30 x 7 = 210

30 - 28 = 2

2 x 7 = 14

therefore 28 x 7 = 210 - 14 = 196 #

memandangkan 3.5 x 2 = 7

3.5 x 9 = 3.5 x 2 x 4 + 3.5

= 7 x 4 + 3.5

= 28 + 3.5

= 31.5 #

*cara aku kira pantas yg highlight tu je*

complicated, kan?

but this is the way aku congak dari dulu sampai sekarang..

nape complicated sgt pemikiran aku ni ek?

ntah..

Wallahualam..

aku pun x mengerti..

nampak sgt aku ni budak maths yg sgt complicated..

sukar dijelaskan..

kan?

hahahahahahaha..

(^_^)v

>> .........

i'm trying my best..

but i get only this..

maybe my effort is not good enough..

or maybe this is just my limit..

i can't go beyond that..

am i that dumb..??

feel hopeless too this sem..

nooooo....!!!!

>> my exact feelings (life cont)..

bila aku buat, try nk study life contingencies..

aku akan try xnak pikir ape2 yg negatif ke ape..

tanamkan dalam diri..

"boleh buat ni.! liana.. kau boleh..!! chaiyok2..!!"

tapi bila tgh study..

err..

apesal mcm ni..??

tadi aku rase gune formula ni je dah okay..

belek2 lagi..

oo...

oooooo...

boleh paham ni la kot..

dia mcm ni kalau mcm ni..

kalau mcm tu kene modified sikit2..

bla bla bla...

pastu..

bila try buat latihan tanpa belek nota..

dem..!

terasa diri ini terlalu hina..

bengap giler dan sebagainya..

mengapa begini..??

siyes stress..!

terasa tahap kebangangan aku berada di puncak.!

kenapa..?

kenapa..?

dan kenapa..??

kenapa soklan life cont mcm ni..?

 

kenapa aku amek life cont..??

sebab ni subjek wajib bagi course Actuarial Science..

nape aku amek course ni in the first place..??

sbb aku rasa course ni ade masa depan yg cerah utk aku..

tapi skrg..

setelah belajar life cont..

sumenye mcm berubah..

awan yg cerah bertukar menjadi mendung..

petanda mcm nk hujan lebat je.. 

*rasa mcm nk nangis sentiasa..*

ku lihat sekelilingku bagaikan kelam jek..

tiada lagi sinar harapan..

terasa mcm masa depanku musnah dek life cont ni punye keje..

kalau subjek lain..

still okay lagi la..

walaupun aku x terror..

tapi at least when i try harder, i get what i suppose to get..

x dpt A..

dapat B pu jadik la..

tapi life cont ni sewel sikit..

jangankan A..

B puh jauh dari pandangan mata..

ntah mana silapnya..

aku ni 'pandai' sangat ke apa..??

yg buat aku lagi rase down ttg life cont ni..

carry mark mmg xpayah ckp la kan..

teruk nak mampus..

xdapat nk support pun..

ntah la..

rasa mcm nk give up pun ade gak..

dah la sem ni ISM nak minimum gred C..

below C = 0.00

xde scale..

fail..

kene repeat..

haish~

nak kata aku byk main.?

aku byk study kot sem ni..

korea..?

hah..

dah lame aku tinggalkan dunia drama..

just check dbsknights je tiap2 hari mcm aku check blog orang..

dah la dalam actuarial industry ni life cont penting giler2..

mmg dah terasa hati pun nk tukar channel pergi bidang lain..

bidang yg sipi2 tapi xpayah nk gune life cont lagi..

kesimpulannya..

life cont buat aku tukar pikiran ttg dunia ini..

when everyone said actuarial science is a tough courses..

i think its okay..

i can challenge myself to do it..

but now..?

amek kaw..!

life cont.. oh life cont..

aku rasa subjek lain mcm xde la tough giler babeng mcm life cont..

 

yg paling aku takut..

aku cuak life cont..

sampai yg lain2 yg aku agak okay pun aku ter'cuak'kan sekalu jugak..

pastu sume trang tang tang kebaboom..

huwargh..!!

cmne la nk dpt dean list mcm nih..??

=(

soklan macam senang tapi....

L is the loss at issue random variable for a fully discrete whole life insurance of 1 on (x). the annual premium charged for this insurance is 0.044. you are given:

(i) Ax = 0.40

(ii) a double dot x =10

(iii) Var (L) = 0.12

an insurer has a portfolio of 100 such insurances on 100 independent lives. 80 of these insurances have death benefit of 4 and 20 have death benefits of 1. assume that the total loss for this portfolio is distributed normally. calculate the probability that the present value of the gain for this portfolio is greater than 22.

okay..

aku taw ape yg dia nak..

dia nak P(X > 22) 

bila dia ckp assume normally distributed..

so P(X > 22) = P(Z > (22-mean)/standard deviation )

so sebelum dapat probability ikut normal graph tu..

aku kene cari mean ngan variance la dulu..

kan..??

tapi..

mcm mane nk cari mean..??

E(S) = 80x4(__??__) + 20x1(__??__)

cmne pulak nk cari variance..??

Var(S) = (__??__)Var(L) + (__??__)

argh..!!

aku xtaw ape yg patut ade dlm blank tu..!!

hiyargh..!!!

jom bunuh diri same2 nak..??

liana..!!

chill la babe..

okay..

dia  ade kasik Ax ngan a double dot x kan..?

hurm..

daripade 2 bende tu..

ko boleh carik ape..??

yer..

carik la d..

d = (1-Ax)/ a double dot x

tekan calculator..

ko akan dapat d= 0.06

belek la example ke ape..

ko akan jumpe ni..

E(L) = Ax + P a double dot x

so kalau untuk benefits of 1..

kacang je la nk cari E(L)..

sebab dia dah bagi sume..

E(L) = 0.4-0.044(10) = -0.04

kalau benefits of 4..??

kali 4 je ke..??

hurm..

bukan.

kene cari P dia sendiri sebab dia x bagi P ntuk 4..

pastu guna formula yg sama..

E(L) = 4(0.4)- P(10) = __

pastu Var (L) = (1+P/d)^2 * (2kecik Ax - Ax ^2)

bla bla bla..

then aku dapat Var (S) = 11312.704

E(S) = 95.2

masukkan value..

P(Z > (22-95.2)/ sqrt(11312.704))

= P(Z > -0.6822)

= 1 - 0.2547

= 0.7453 #

tapi..

jawapan dia 0.25

grrrrr...

jom bunuh orang yg buat soklan ni..!!

>> maths & love story..

math tells us 3 of the saddest love stories:

1) of parallel lines, who are never meant to meet.

2) of tangent lines, who were together once then parted forever.

3) and of asymptotes, who could only get closer and closer, but could never be together.

 

 sad, isn't it..??

:')

>> life contingencies [1]..

another LC question..

you are given:

- 2 states

  -> preferred with annual expected losses of 400

  -> standard with annual expected losses of 900

- no change in the expected losses for either class over the next 3 years

- the transition matrix

     0.85   0.15

     0.60   0.40

- i = 0.05

- no expenses

- losses are paid at the end of the year

- all insured remain insured for following 3 years

calculate the 3 year term insurance single benefit premium for a standard driver

okay..

soalan ni dia mintak SBP kan..?

so..

mmg berguna nombor 400 & 900 tu..

baru aku paham..

no tu digunakan utk cari SBP (single benefit premium) or APV (actuarial present value)..

untuk menjawab soalan di atas..

seperti biase..

kene cari 2Q(2,1) dulu..

2Q(2,1) = [ 0.6  0.4] [ 0.85  0.15 ] = [ 0.75  0.25]

                        0.60  0.40  

untuk cari SBP standard driver for 3 year term insurance..

guna formula ni..

SBP = (b^t standard)*v + (b^t Q(2,1))* v^2 + (b^t 2Q(2,1))* v^3 

    = 900*((1.05)^-1) + (400*0.6+900 *0.4)*((1.05)^-2) 

      + (400*0.75+900*0.25)* ((1.05)^-3)

    = 1895 #

yes..

the answer is 1895..

the thing that i wonder now is..

what is the function of having this words?

losses are paid at the end of the year

term insurance

i mean..

is it the same kind of technique and formula if they give

'paid at the beginning of the year'

'whole life insurance', 'endowment insurance', etc..??

hurm..

lets study more..

(^_^)v

>> 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..

>> musim test lagi..

16 MAC 2011

EXCEL

9-10am

21 or 23 MAC 2011

PROBABILITY & STATISTICS 2

10-11 am

24 MAC 2011

MONTE CARLO SIMULATION METHOD

4-5pm

29 MAC 2011

FURTHER LIFE CONTINGENCIES

10-11am

30 MAC 2011

SURVIVAL DATA ANALYSIS

11-12pm

huhuuhuu.

test pun mcm final dah nie..

gilo aku mcm ni..

mak hai~

nak balik..!!

>.<"

>> the beauty of mathematics & love of God..

Here is an interesting and lovely way to look at the beauty of mathematics, and of God, the sum of all wonders.

1 x 8 + 1 = 9

12 x 8 + 2 = 98

123 x 8 + 3 = 987

1234 x 8 + 4 = 9876

12345 x 8 + 5 = 98765

123456 x 8 + 6 = 987654

1234567 x 8 + 7 = 9876543

12345678 x 8 + 8 = 98765432

123456789 x 8 + 9 = 987654321

 1 x 9 + 2 = 11

12 x 9 + 3 = 111

123 x 9 + 4 = 1111

1234 x 9 + 5 = 11111

12345 x 9 + 6 = 111111

123456 x 9 + 7 = 1111111

1234567 x 9 + 8 = 11111111

12345678 x 9 + 9 = 111111111

123456789 x 9 +10= 1111111111

9 x 9 + 7 = 88

98 x 9 + 6 = 888

987 x 9 + 5 = 8888

9876 x 9 + 4 = 88888

98765 x 9 + 3 = 888888

987654 x 9 + 2 = 8888888

9876543 x 9 + 1 = 88888888

98765432 x 9 + 0 = 888888888

Brilliant, isn’t it?

And look at this symmetry:

 1 x 1 = 1

11 x 11 = 121

111 x 111 = 12321

1111 x 1111 = 1234321

11111 x 11111 = 123454321

111111 x 111111 = 12345654321

1111111 x 1111111 = 1234567654321

11111111 x 11111111 = 123456787654321

111111111 x 111111111 = 12345678987654321

Now, take a look at this…

101%

From a strictly mathematical viewpoint:

What Equals 100%?

What does it mean to give MORE than 100%?

Ever wonder about those people who say they are giving more than 100%?

We have all been in situations where someone wants you to

GIVE OVER 100%.

How about ACHIEVING 101%?

What equals 100% in life?

Here’s a little mathematical formula that might help

Answer these questions:

If:

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Is represented as:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26.

If:

H-A-R-D-W-O-R- K

8+1+18+4+23+15+18+11 = 98%

And:

K-N-O-W-L-E-D-G-E

11+14+15+23+12+5+4+7+5 = 96%

But:

A-T-T-I-T-U-D-E

1+20+20+9+20+21+4+5 = 100%

THEN, look how far the love of God will take you:

L-O-V-E-O-F-G-O-D

12+15+22+5+15+6+7+15+4 = 101%

Therefore, one can conclude with mathematical certainty that:

While Hard Work and Knowledge will get you close, and Attitude will

Get you there, It’s the Love of God that will put you over the top!

Sent by brother Ameer via email. May Allah bless him for his kindness :)

Ya Haqq,

http://darvish.wordpress.com/2008/03/16/the-beauty-of-mathematics-and-the-love-of-god/