Probability & Counting (Advanced)

Probability & Counting: core idea

• 1. Hypergeometric: 5 red in 10, draw 2: $P(\text{both red})$?

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• 2. Bayes: prior $1/2$, likelihoods $0.8$ and $0.4$: posterior for first hypothesis given positive? Enter as reduced fraction $a/b$ of form?

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• 3. Derangements $!3$?

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• 4. Geometric $p=1/2$: $P(X=3)$ first success on 3rd?

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• 5. Var of die roll $1..6$?

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• 6. Poisson $\lambda=2$: $P(X=0)$?

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• 7. Cov of independent X,Y?

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• 8. Negative binomial: trials until 2nd success $p=1/2$: $P(X=3)$?

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• 9. Markov: from A stay 0.7, to B 0.3; start A: $P(A)$ after 1 step?

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