Matakuliah
Tahun
Versi
: H0332/Simulasi dan Permodelan
: 2005
: 1/1
Pertemuan #2
Probability and Statistics
1
Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
• Mahasiswa dapat menggunakan teori
probabilitas dan statistik (C3)
2
Outline Materi
• Konsep dasar probability and statistics
3
Konsep dasar
• Denote random variable X, Y, Z
• The value of random variable x, y, z
• The distribution function (the cumulative distribution function)
F ( x)  P( X  x)
b
P( X  I )   f ( y)dy  F (b)  F (a)
a
• The probability that the discrete random variable X takes on
the value x
p( xi )  P( X  xi )

 p( x )  1
i 1
i
4
Konsep dasar
• The joint probability mass function of X and Y
p ( x, y )  P ( X  x, Y  y )
for all
x, y
• X and Y are independent if
p( x, y)  pX ( x) pY ( y)
for all
x, y
• Mean or expected value

 x j p X i ( x j )
 j 1
i   
 xf ( x)dx
  Xi
 
if Xi is discrete
if Xi is continuous
5
Konsep dasar
• Expected-value’s properties
E (cX )  cE ( X )
 n
 n
E   ci X i    ci E  X i  even if the Xi’s are dependent
 i 1
 i 1
• Variance

  
Var ( X i )   i2  E  X i  i   E X i2  i2
2
• Variance’s properties
Var ( X )  0
Var (cX )  c 2Var ( X )
 n
 n
Var  X i   Var  X i  if the Xi’s are independent
 i 1  i 1
6
Konsep dasar
• The standard deviation

  
Var ( X i )   i2  E  X i  i   E X i2  i2
2
• The covariance


Cij  E  X i  i X j   j   E X i X j   i  j
• The correlation
ij 
Cij
 i2 2j
7