Chapters

0 ≤ p(A) ≤ 1

p(S) = 1

Probability Formula

Addition Rule

If A B ≠ .

p(A ∪ B) = p(A) + p(B) − p(A B)

p(A ∪ B ∪ C) = p(A) + p(B) + p(C) − p(A B) − p(A C) − p(B C) + p(A B C)

Multiplication Rule

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Independent Events

p(A B) = p(A) · p(B)

Dependent Events

p(A B) = p(A) · p(B|A)

Conditional Probability

Independent Events

p(A|B) = p(A)

Dependent Events

p(A|B) ≠ p(A)

Law of Total Probability

p(B) = p(A1) · p(B|A1) + p(A2) · p(B|A2 ) + ... + p(An) · p(B|An )

Bayes' Theorem

Expected Value

Variance of a Discrete Random Variable

Standard Deviation of a Discrete Random Variable

Binomial Distribution

Normal Approximation to the Binomial

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Emma

Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.