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Mathematics · University

Conditional probability and expectation · revision notes

P(A∣B)=P(A and B)/P(B) requires P(B)>0.

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Key ideas and conditions

Conditioning

P(A∣B)=P(A and B)/P(B) requires P(B)>0.

Independence

A and B are independent when P(A and B)=P(A)P(B); independence is not the same as disjointness.

Expectation

Expectations add even without independence, provided the relevant expectations exist.

Variance

Variance adds for independent variables; in general include covariance terms.

Explain without looking

  1. X is binomial with n=10 and p=0.3. Find its variance.
  2. Explain why reversing a conditional probability without adjusting for base rates is generally wrong.

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