Midterm CheatSheet
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1 Conditional Probabili ty • 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 (A c |B) = P (B|A) P (B|A c ) P (A) P (A c ) • 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|A i , E )P (A i |E ) • Disjoint vs Independence P (A ∩ B) = 0 (Disj oint ) P (A ∩ B) = P (A)P (B) (Independent) • If A and B are independent, then A and B c , A c and B, A c and B c are also independent. 2 1
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Stat 110
Transcript of Midterm CheatSheet
7/17/2019 Midterm CheatSheet
http://slidepdf.com/reader/full/midterm-cheatsheet-568d4a3a19074 1/1
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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