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23D The Binomial Distribution

23D The Binomial Distribution . Ch. 15H continued. -applied to experiments with replacement ONLY(therefore…..independent events only) -Note: For DEPENDENT events we use the “ hypergeometric probability distribution ” (Not part of SL course but included for your mathematical enjoyment)

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23D The Binomial Distribution

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  1. 23D The Binomial Distribution Ch. 15H continued

  2. -applied to experiments with replacement ONLY(therefore…..independent events only) • -Note: For DEPENDENT events we use the “hypergeometric probability distribution” (Not part of SL course but included for your mathematical enjoyment) • 2 Possible outcomes • SUCCESS = the event happens • FAILURE = the event does not happen The Binomial Distribution

  3. When the experiment is repeated a number (n) of independenttrials, we call it a binomial experiment. • Probability for successes (p) is CONSTANT (independent events) • Probability for failure = 1-p (complimentary) • Random variable X = number of successes in n trials The Binomial Distribution

  4. For n trials r SUCCESSES and n-r failures in an experiment • where r = 0,1,2,3, …………….,n • We call P(X = r) the binomial probability distribution function • NOTE: The Binomial Distribution

  5. NOTE: • Vs. Why the switch in order?!?!

  6. Note WE have to flip to 0,1,2,3,4,5

  7. NOTE: • Vs. Why the switch in order?!?!

  8. All this does is reverse the order of the expansion……thus for

  9. Which makes more sense when graphing

  10. The expected outcome of the experiment is the population mean: The Binomial Distribution

  11. If X is the random variable for a binomial experiment with parameters n and p, the we write • Note: The squiggly is read “is distributed as • X(the random variable) is distributed as a binomial with n trials and a probability of success = p. The Binomial Distribution

  12. Normally Distributed Skewed (+ or -)

  13. Graphics Display Calculator • Binomial probability distribution function (binompdf) • Use to find P(X=r) (exactly) • Binomial cumulative distribution function • (binomcdf) • Use to find

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