Matakuliah
Tahun
Versi
: H0332/Simulasi dan Permodelan
: 2005
: 1/1
Pertemuan #3
Probability Distribution
1
Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
• Mahasiswa dapat menghubungkan
probability distribution dengan fenomena
yang sesuai (C4)
2
Outline Materi
•
•
•
•
Uniform, U(a,b)
Exponential, expo(b)
Normal, N(m, s 2)
Poisson, Poisson(l)
3
Uniform, U(a,b)
Used as a “first” model for a quantity that is felt to be randomly
varying between a and b but about which little else is know. The
U(a,b) distribution is essential in generating random values from
all other distributions.
Density
 1
if a  x  b

f ( x)   b  a
0 otherwise
Mean
ab
2
Distribution
0 if x  a
 1

F ( x)  
if a  x  b
b  a
1 if b  x
Variance
a  b 2
12
4
Uniform, U(a,b)
5
Exponential, expo(b)
Interarrival times of “customers” to a system that
occur at a constant rate.
Density
 1  bx
if x  0
 e
f ( x)   b
0 otherwise

Mean
b
Distribution
x


b

if x  0
F ( x)  1  e
0 otherwise
Variance
b2
6
Exponential, expo(b)
7
Normal, N(m, s 2)
Errors of various types, e.g., in the impact point of a
bomb, quantities that are the sum of a large number
of other quantities (by virtue of central limit theorems)
Density
f ( x) 
1
2s 2

e
 x  m 2
2s 2
Mean
m
Distribution
no closed form
Variance
s2
8
Normal, N(m, s 2)
9
Poisson, Poisson(l)
Number of events that occur in an interval of time when the
events are occuring at a constant rate; number of items in a
batch of random size; number of items demanded from an
inventory
Density
 e  l lx
if x  0,1,...

f ( x)   x!
0 otherwise

Mean
l
Distribution
0 if x  0

F ( x)   l  x  li
e  i! if x  0
 i 0
Variance
l
10
Poisson, Poisson(l)
11