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Unformatted text preview: ent “the sum is less than 5”? 12 Example: Rolling two dice What is the probability of the event “the sum is less than 5”?
Die 2
1
Die 1 1
2
3
4
5
6 P(“sum less than 5”) = 6/36 = 1/6 2 3 4 5 6 13 Views of Probability frequentist view: relative frequency
NA
n−>∞ N P (A) = lim N number of experiments
NA number of experiments where A happened
Bayesian view: degree of belief
“What is the probability that there is life on Mars” 14 Bayesian probability From Wikipedia, the free encyclopedia.
Bayesianism is the philosophical tenet that the mathematical theory of probability
applies to the degree of plausibility of statements, or to the degree of belief of
rational agents in the truth of statements. This is in contrast to frequentism,
which rejects degreeofbelief interpretations of mathematical probability, and
assigns probabilities only to random events according to their relative frequencies
of occurrence. The Bayesian interpretation of probability allows probabilities
assigned to random events, but also allows the assignment of probabilities to any
other kind of statement. Whereas a frequentist and a Bayesian might both assign
probability 1/2 to the event of getting a head when a coin is tossed, a Bayesian
might assign probability 1/2 to personal belief in the proposition that there was
life on Mars a billion years ago, without intending to assert anything about any
relative frequency. 15 Conditional Probability How does one event occuring aﬀect the chance of occurence of another event
occuring.
“What is the probability of voting for Romney, given that you have an income of
over 1 million dollars?”
Probability of A given B P (AB ) = P (A, B )
P (B ) 16 Jochen’s dice example What is P(D1=1,D2=2)? 17 Jochen’s dice example
Die 2
1 2 3 4 5 6 Die 1 1
2
3
4
5
6 What is P(D1=1,D2=2)? 1/36 18 Jochen’s dice example What is P(D1=1,D2=2)? 1/36
What is P(D1=1  D2=2)? 19 Jochen’s dice example
Die 2
1 2 3 4 5 6 Die 1 1
2
3
4
5
6 What is P(D1=1,D2=2)? 1/36
What is P(D1=1  D2=2)? 1/6 20 Jochen’s dice example What is P(D1=1,D2=2)? 1/36
What is P(D1=1  D2=2)? 1/6
What is P(D1=1  sum is even)? 21 Jochen’s dice example
Die 2
1 2 3 4 5 6 Die 1 1
2
3
4
5
6 What is P(D1=1,D2=2)? 1/36
What is P(D1=1  D2=2)? 1/6
What is P(D1=1  sum is even)? 3/18=1/6 (sum is even along alternating
diagonals) 22 Jochen’s dice example What is P(D1=1,D2=2)? 1/36
What is P(D1=1  D2=2)? 1/6
What is P(D1=1  sum is even)? 3/18=1/6 sum is even along alternating
diagonals
What is P(D1=1  sum is 4)? 23 Jochen’s dice example
Die 2
1 2 3 4 5 6 Die 1 1
2
3
4
5
6 What is P(D1=1,D2=2)? 1/36
What is P(D1=1  D2=2)? 1/6
What is P(D1=1  sum is even)? 3/18=1/6 sum is even along alternating
diagonals
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This note was uploaded on 02/09/2014 for the course COGS 109 taught by Professor Staff during the Fall '08 term at UCSD.
 Fall '08
 staff

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