7/17/2019 Midterm CheatSheet

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1 Conditional Probability

•   Bayes’ Rule

P (A ∩B) = P (B)P (A|B) = P (A)P (B|A)

•   Bayes’ Rule Odd form:

Odd(A|B) =  P (A|B)

P (Ac|B) =

  P (B|A)

P (B|Ac)

P (A)

P (Ac)

•  Conditional probability satisfies all the properties of probability.

P (A|B, E ) = P (B|A,E )P (A|E )

P (B|E )

P (B|E ) =

n

i=1

P (B|Ai, E )P (Ai|E )

•   Disjoint vs Independence

P (A ∩B) = 0 (Disjoint)

P (A ∩B) = P (A)P (B) (Independent)

•   If  A  and  B  are independent, then  A  and  Bc,  Ac and  B,  Ac and  Bc arealso independent.

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