Class notes for ECEN 305 Probability Theory

I Outcome
Octerministic :


non-deterministic : Manydvscomes


Outcome : result of landom experiment
sample space : all Possible outcomes
Event" subspace of sample Stace

Probability CXIOMS :
·
0 P(K] = / OUTCOM2 probability is between
I
zero and
· P[S] =


·
P(X ,
or x2] = P(x ],
+ P[xz] our comes Can't huppen
Simultaniously

Receive frequency : N: amount of specific
CrTCOM2

weak law Px n:
:
simfx(n) = Total Trials

no


Random experiment :
· Repeatable
·
know all Assible Outcomes
· outcomes can be assigned Probabilities


complementary Evenis : A happens When A does not happen.
Mutually excirsive and collectively exiusive.

, -




Union : Aug A 8 or both
Intersection : And A and 8
S

complement : A Olloste Of A ↓


subser A cg A occurs with o

Jenayans :
(ARO" : Ave
Eveni space : Mutually exclusive
A: CUCUCzUCy
events of S
a ambe

Space ,




ex .
Toss Par Coins Observe heads or fails .
,

find probability for a set ofcutcomes with < 3 heads.
OUT COMES :

TT + T & Evenis : 1 ,
2, 3
, 11 heads
+ + + no 1 , 2 , 3 4 Tails
,
T nTa
TT
ThTTa
Probability per cain :
In a It
↑ Tho
That
Probability for 1 head/tais
Thnn o


P(in) P(za)
⑧

UTTT &
PLA) = P(On) + +



to + +=
nTTHa =
Nrh5 o


ninn
unit 6


nuth
unut
Annn