Binomial Distribution

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Poker Hands • how many possible hands? ⎛52⎞ 52! ⎜ ⎟= = 2,598,960 ⎝ 5 ⎠ 5!47! – roughly 4 in 10 million • one pair, with 3 different remaining cards – number of ways to have a pair – number of ways to have the remaining cards ⎛4⎞ 3 ⎛12⎞ 13⎜ ⎟4⎜ ⎟ 2 3 p(one pair) = ⎝ ⎠ ⎝ ⎠ ≈.42 ⎛52⎞ ⎜ ⎟ ⎝ 5 ⎠ • full house (.0014)? flush? (.00198) nothing? ⎛4⎞ 13⎜ ⎟ ⎝2⎠ ⎛12⎞ (4)(4)(4) ⎜ ⎟ ⎝ 3 ⎠
Bernoulli Trials • For Bernoulli process, just two event classes (e.g., coin flip) – p = success – q = failure = 1-p – stationary versus non-stationary – not all orders are equally probable (depends on p) – for independent stationary, the probability of a particular (ordered) sequence of N trials • prqN-r , where r is number of successes • same probability for all orders giving with this number of successes – often we want to know the probability of r successes, regardless of order ⎛N⎞ ⎜ ⎟ pq ⎝ r ⎠ • multiply by the number of orders r N−r
Page 1 and 2: Binomial Distribution (discrete ran
Page 3: • Ordered Combinations - Selectin
Page 7 and 8: Probabilities of Intervals for Bino
Page 9: Sign Test for 2 Matched Groups •

Binomial Distribution

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