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2010
ECE500:Discrete Mathematics BAYESIAN PROJECT: Title kita Rokok?
LECTURER: HASMILA AKMAR OMAR
MEMBER MOHD FARIS BIN DOLAMAHPUL 2009717537
MEMBER MOHD AZHAR BIN ABDULLAH 2009937901
MEMBER MUHAMMAD AZRI BIN ABDUL KUDUS 2009546345
MEMBER HAIRUL HAZWAN BIN HAIRUDDIN 2009722949
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INTRODUCTION
Bayesian statistics is concerned with generating the posterior distribution of the unknown
parameters given both the data and some prior density for these parameters. As such, Bayesian
statistics provides a much more complete picture of the uncertainty in the estimation of the
unknown parameters, especially after the confounding effects of nuisance parameters areremoved. Bayesian is used to determine the probability of event occurring while another event
has already occurred. It is also called Conditional Probability. The Bayesian formula given:
P(B|A) = P(A and B) / P(A)
A is the event that already occurred, while B is event that is occurring. The sample spaced has
become smaller since event A has already occurred. Therefore, event B occur base on the
sample space A.
*kena tukar In this Bayesian project, our study case is on Alarm System. The alarm is placed at home. The
function of the alarm is to tell if the house is in danger. There are 4 things that can cause the
alarm to trigger which are Burglary, Earthquake, Tsunami and Strom. By using Bayesian
method we determine how many times the alarm will be triggered in 30 days (a month). We also
calculated the probability that Burglary, Earthquake, Tsunami and Storm will happened. Below
is the connection between Alarm, Burglary, Earthquake, Tsunami and Strom:
Diagram: Show the relationship between Alarm, Burglary, Earthquake, Tsunami and Storm.
Burglary
Tsunami
Alarm
Earthquake
Storm
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THE ALARM DATA
Table: The probability event occurs.
Burglary Earthquake Tsunami Storm Alarm
Yes No Yes No Yes No Yes No Yes
True 8 12 True 4 9 True 6 10 True 7 11 12 18
False 4 6 False 8 9 False 6 8 False 5 7
True 8/12 12/18 True 4/12 9/18 True 6/12 10/18 True 7/12 11/18 12/30 18/30
False 4/12 6/18 False 8/12 9/18 False 6/12 8/18 False 5/12 7/18
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CALCULATION
COMPUTING THE PROBABILITY FOR ALARM = YES
P(Burglary = true|alarm= yes)= 8/12
P(Earthquake = true|alarm=yes)= 4 / 12
P(Tsunami= true|alarm=yes)= 6 / 12
P(Storm= true|alarm= yes)= 7 / 12
P(alarm=yes)= 12 / 30
P( E| alarm=yes)* P( alarm=yes) =(8 / 12)(4 / 12)(6 / 12)(7 / 12)(12 / 30)=0.0259
P( E| alarm=no)* P( alarm=no) =(12 / 18)(9 / 18)(10 / 18)(11 / 18)(18 / 30)=0.0679
0.0259<0.0679
F or the new day no is more likely than yes