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4-2_binrv

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

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Binomial Random Variables Binomial Probability Distributions

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“2-outcome” situations are very common Heads/tails Democrat/Republican Male/Female Win/Loss Success/Failure Defective/Nondefective
Probability Model for this Common Situation Common characteristics repeated “trials” 2 outcomes on each trial Leads to Binomial Experiment

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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 The binomial random variable x is the number of “successes” in the n trials

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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 Distribution ( 29 ( 29 [ ] npq x E x Var np q p x x xp

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