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4-2_binrv

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

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Binomial Random Variables Binomial Random Variables Binomial Probability Distributions

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Binomial Random Binomial Random Variables Variables Through 2/24/2011 NC State’s 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

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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

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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

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Binomial Probability Binomial Probability Distribution Distribution ( 29 0 0 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
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4-2_binrv - Binomial Random Variables Binomial Probability...

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