section4_handout_stat104_josh

section4_handout_stat104_josh - Stat 104 Section 2 Josh...

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Stat 104 Section 2 Josh Zagorsky < zagorsky@fas.harvard.edu > From P-Set #3 1. The intersection of two sets is anything that’s a member of both. The union of two sets is anything that’s a member of at least one. 2. A simulation usually involves doing a random experiment many times and tallying the results. Concepts 1. Remember Bayes’ Rule from last time: P ( A | B ) = P ( B | A ) P ( A ) P ( B ) 2. Expected Value is the average outcome value of an experiment. 3. Binomial Distribution μ = np σ = p np (1 - p ) Probability of k successes in n trials = ( n k ) p k (1 - p ) n - k = n ! k !( n - k )! p k (1 - p ) n - k Use Stata command display binomial(n,k,p) to find the probability that there are at most k successes in n trials with a success probability of p . To find the probability of exactly k successes in n trials, use display binomial(n,k,p) - binomial(n,k-1,p) 1
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Practice Problems: 2) Powerball (See http://www.powerball.com/powerball/pb_prizes.asp for more info) In the national “Powerball” lottery system, 5 distinct balls are selected out of a drum of 59 white balls (without replacement), and 1 red ball is independently selected from a different drum with 39 balls. In order to win the variable-amount jackpot, you must match all 5 drawn white balls, in any order, and the red ball exactly. a) Verify that the probability of winning the jackpot is 1/195,249,054
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This note was uploaded on 03/27/2012 for the course STATS 104 taught by Professor Michaelparzen during the Fall '11 term at Harvard.

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section4_handout_stat104_josh - Stat 104 Section 2 Josh...

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