Download - 23D The Binomial Distribution
![Page 1: 23D The Binomial Distribution](https://reader035.vdocument.in/reader035/viewer/2022062222/56815eeb550346895dcda2ab/html5/thumbnails/1.jpg)
Ch. 15H continued
*23D The Binomial Distribution
![Page 2: 23D The Binomial Distribution](https://reader035.vdocument.in/reader035/viewer/2022062222/56815eeb550346895dcda2ab/html5/thumbnails/2.jpg)
*The Binomial Distribution*-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
![Page 3: 23D The Binomial Distribution](https://reader035.vdocument.in/reader035/viewer/2022062222/56815eeb550346895dcda2ab/html5/thumbnails/3.jpg)
*The Binomial Distribution*When the experiment is repeated a number (n) of
independent trials, 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
![Page 4: 23D The Binomial Distribution](https://reader035.vdocument.in/reader035/viewer/2022062222/56815eeb550346895dcda2ab/html5/thumbnails/4.jpg)
*The Binomial Distribution*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:
![Page 5: 23D The Binomial Distribution](https://reader035.vdocument.in/reader035/viewer/2022062222/56815eeb550346895dcda2ab/html5/thumbnails/5.jpg)
*
*NOTE:
* Vs.
Why the switch in order?!?!
![Page 6: 23D The Binomial Distribution](https://reader035.vdocument.in/reader035/viewer/2022062222/56815eeb550346895dcda2ab/html5/thumbnails/6.jpg)
Note WE have to flip to 0,1,2,3,4,5
![Page 7: 23D The Binomial Distribution](https://reader035.vdocument.in/reader035/viewer/2022062222/56815eeb550346895dcda2ab/html5/thumbnails/7.jpg)
*
*NOTE:
* Vs.
Why the switch in order?!?!
![Page 8: 23D The Binomial Distribution](https://reader035.vdocument.in/reader035/viewer/2022062222/56815eeb550346895dcda2ab/html5/thumbnails/8.jpg)
*All this does is reverse the order of the expansion……thus for
![Page 9: 23D The Binomial Distribution](https://reader035.vdocument.in/reader035/viewer/2022062222/56815eeb550346895dcda2ab/html5/thumbnails/9.jpg)
*Which makes more sense when graphing
![Page 10: 23D The Binomial Distribution](https://reader035.vdocument.in/reader035/viewer/2022062222/56815eeb550346895dcda2ab/html5/thumbnails/10.jpg)
*The Binomial Distribution*The expected outcome of the experiment is the
population mean:
![Page 11: 23D The Binomial Distribution](https://reader035.vdocument.in/reader035/viewer/2022062222/56815eeb550346895dcda2ab/html5/thumbnails/11.jpg)
*The Binomial Distribution
*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.
![Page 12: 23D The Binomial Distribution](https://reader035.vdocument.in/reader035/viewer/2022062222/56815eeb550346895dcda2ab/html5/thumbnails/12.jpg)
Normally Distributed Skewed (+ or -)
![Page 13: 23D The Binomial Distribution](https://reader035.vdocument.in/reader035/viewer/2022062222/56815eeb550346895dcda2ab/html5/thumbnails/13.jpg)
*Graphics Display Calculator
*Binomial probability distribution function (binompdf) *Use to find P(X=r) (exactly)
*Binomial cumulative distribution function*(binomcdf)*Use to find