Class notes INDE315 Applied Statistics and Probability for Engineers

CHAPTER 2
( S ) P ( s)
sample space : = 1




set of all possible outcomes of a random experimeut
Event subset of the
sample space ( E )


PLAM
且
P LA | B )
P (B )
时
givem

PLE ) should satisfy O ≤ PLE ) ≤ 1


P (s ) =


ifE ,
Λ E 2 =φ→ PLE ,
UE 2 } =
PLE .
3 + PCE ]
2




LA A ]
complement , A ,




' '
( E . UE 2 } ) =
E UE,
2




STEPS → UULTIPLICATION RULE

H
ways fo completug step 1 Drow tree
diagram
Hz for step 2

u 3 和fo step 3
…
…




total = n . XUzxu …




ORDER → PERMUTATION RLLE
MATTER Uniqme sequance order matters ! wlo replacement
过的元素不能再
# of permntation fora setof u items usu !
0 ! = 1




《
二
用 用

, eg componen
4 ,
how
otcatios many
combinaton ' s ?



p% = P4 :

)! = 1080




for similar objeatslr areiodenticall ※U
usharbly biggez s


thau r
U = U , + Mz + M + ur
3
…




h. icdentical 业
Uzidantical U , ! M2 ! …
hr !

…




ORDERPUESN ' → CUUBINATION RULE
T




UATTER
order odoesu't matter choose r from u
,


# P > #C

cr
刁
=
( q) =


箭! n "
-




u Cr



soumple uwforeplacewrent




→ C位 =
無 :
= 3


47 !
→ C = 4


:4 =
!
118365




iseleto
E = 3× 178365 :
53509


orwt of 50 C∵


def |samp 6 经
:
P (2 ) :
3 .
49
0
C




。一

, LECTURE 2
Addition Rule

P (σ UB ) =
PCA ) + P ( B) -
P [ AMB )

P ( AMB ) =
P (A ) + PB ) -

P [ AUB )



Couditional
Probability



)
Rule
Pro bability ofB given A
Can be writtenas
P < AMB )
PCBIA >= frP (A ) >
)
PCA


Multiplication Rule


P [ AMB ) =
P ( B 1 A] XPCA3
=
P (A | B ) × P [B )




Total
ProbabilityRule
P (B ) = PCBMA ) + PEBMA ' ]

P ( BIA ] PCBIA ) PLA ')
'
= × P ( )+ A




Indepeudence
Mutually Exclusive
if indepencleuce
A happen wornt affectB
'




P ( AMB > =
必
① P (A 1 B> =
PEA )


② P (A =
B P ( A) XP < B )




DeMorgan ' s Law


IB) = ' UB
箱B ,
'


(A A




AUB ) 与 MB
'


=




More than 1 - PL ≤ )
三
=




At least = 1 -

P ( < )

P ()
乏
most
>

At = 1 -




Less than = -
P ( ), )



入