4-2_binrv - Binomial Random Variables Binomial Random...

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Unformatted text preview: Binomial Random Variables Binomial Random Variables Binomial Probability Distributions Binomial Random Binomial Random Variables Variables Through 2/24/2011 NC States free-throw percentage is 69.6% (146 th out 345 in Div. 1). If in the 2/26/2011 game with GaTech, NCSU shoots 11 free-throws, what is the probability that: NCSU makes exactly 8 free-throws? NCSU makes at most 8 free throws? NCSU makes at least 8 free-throws? 2-outcome situations are very 2-outcome situations are very common common Heads/tails Democrat/Republican Male/Female Win/Loss Success/Failure Defective/Nondefective Probability Model for this Probability Model for this Common Situation Common Situation Common characteristics repeated trials 2 outcomes on each trial Leads to Binomial Experiment Binomial Experiments Binomial Experiments n identical trials n specified in advance 2 outcomes on each trial usually referred to as success and failure p success probability; q=1-p failure probability; remain constant from trial to trial trials are independent Binomial Random Variable Binomial Random Variable The binomial random variable X is the number of successes in the n trials Notation: X has a B(n, p) distribution, where n is the number of trials and p is the success probability on each trial. Examples Examples a. Yes; n=10; success=major repairs within 3 months; p=.05 b. No; n not specified in advance c. No; p changes d. Yes; n=1500; success=chip is defective; p=.10 Binomial Probability Binomial Probability Distribution Distribution ( 29 trials, success probability on each trial probability distribution: ( ) , 0,1,2, , ( ) ( ) ( ) ( x n x n x n n n x n x x x x n p p x C p q x n E x xp x x p q np Var x E x npq -- = = 2 = = = = = = = - 29 = K P ( x ) = p x q n-x n !...
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This note was uploaded on 02/13/2012 for the course BUS 350 taught by Professor Reiland during the Fall '08 term at N.C. State.

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4-2_binrv - Binomial Random Variables Binomial Random...

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