Tutorial on Tukey Charts Farrokh Alemi, Ph.D. Sunday, 11/25/2007.
DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.
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Transcript of DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.
![Page 1: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/1.jpg)
DISCRETE PROBABILITY DISTRIBUTIONS
Farrokh Alemi Ph.D.
![Page 2: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/2.jpg)
BernoulliGeometricBinomialPoisson
Discrete Probability Distributions
![Page 3: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/3.jpg)
Density function
Definitions
![Page 4: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/4.jpg)
Cumulative probability function
Definitions
![Page 5: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/5.jpg)
Definitions
![Page 6: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/6.jpg)
Expected Value
![Page 7: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/7.jpg)
Expected Value
![Page 8: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/8.jpg)
Expected Value
![Page 9: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/9.jpg)
Expected Value
![Page 10: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/10.jpg)
Example
![Page 11: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/11.jpg)
Example
![Page 12: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/12.jpg)
Example
![Page 13: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/13.jpg)
Example
10Otherwise
10.042 medication errors
0.960.221 medication error
0.740.740 medication errors
Cumulative distribution
function
Probability density functionEvents
10Otherwise
10.042 medication errors
0.960.221 medication error
0.740.740 medication errors
Cumulative distribution
function
Probability density functionEvents
![Page 14: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/14.jpg)
Example
![Page 15: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/15.jpg)
Example
![Page 16: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/16.jpg)
Density & Cumulative Distributions
![Page 17: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/17.jpg)
BernoulliGeometricBinomialPoisson
Typical Probability Density Functions
![Page 18: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/18.jpg)
Mutually exclusive
Bernoulli Probability Density Function
![Page 19: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/19.jpg)
Exhaustive
Bernoulli Probability Density Function
![Page 20: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/20.jpg)
Bernoulli Probability Density Function
pOccurs
1-PDoes not occur
Probability density functionEvents
pOccurs
1-PDoes not occur
Probability density functionEvents
![Page 21: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/21.jpg)
Bernoulli Probability Density Function
![Page 22: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/22.jpg)
Independent Bernoulli Trials
![Page 23: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/23.jpg)
Independent Bernoulli Trials
![Page 24: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/24.jpg)
Geometric Density Function
![Page 25: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/25.jpg)
Geometric Density Function
![Page 26: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/26.jpg)
Geometric Density Function
![Page 27: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/27.jpg)
No medication errors have occurred in the past 90 days. What is the maximum daily probability of medication error in our facility?
Do One
![Page 28: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/28.jpg)
The time between patient falls was calculated to be 3 days, 60 days and 15 days. What is the daily probability of patient falls?
Do One
![Page 29: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/29.jpg)
Number of k occurrences of the event in n independent trials
Binomial Probability Distribution
![Page 30: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/30.jpg)
Independent Bernoulli Trials
![Page 31: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/31.jpg)
Independent Bernoulli Trials
![Page 32: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/32.jpg)
Independent Bernoulli Trials
![Page 33: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/33.jpg)
Independent Bernoulli Trials
P x (1-P) x P
![Page 34: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/34.jpg)
Different combinationsSuccess probabilitiesFailure probabilities
Binominal Probability Distribution
![Page 35: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/35.jpg)
Binomial Probability Distribution
![Page 36: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/36.jpg)
Binomial Probability Distribution
![Page 37: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/37.jpg)
Binomial Probability Distribution
![Page 38: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/38.jpg)
6 Trials of Binomial p=1/2
![Page 39: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/39.jpg)
6 Trials of Binomial p=1/2
![Page 40: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/40.jpg)
6 Trials of Binomial p=0.05
![Page 41: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/41.jpg)
If the monthly probability of elopement is 0.05, how many patients will elope in 2 years?
Example
![Page 42: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/42.jpg)
If the monthly probability of elopement is 0.05, how many patients will elope in 2 years?
Example
![Page 43: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/43.jpg)
If the daily probability of death due to injury from a ventilation machine is 0.002, what is the probability of having 1 or more deaths in 30 days?
Example
![Page 44: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/44.jpg)
If the daily probability of death due to injury from a ventilation machine is 0.002, what is the probability of having 1 or more deaths in 30 days?
Example
![Page 45: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/45.jpg)
Which is more likely, 2 patients failing to comply with medication orders in 15 days or 3 patients failing to comply with medication orders in 30 days.
Do One
![Page 46: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/46.jpg)
Large number of trialsSmall probabilities of occurrence
Poisson Density Function
![Page 47: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/47.jpg)
Poisson Density Function
k
![Page 48: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/48.jpg)
Poisson Density Function
k
![Page 49: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/49.jpg)
Repeated independent Bernoulli trials is the foundation of many distributions
Take Home Lesson
![Page 50: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/50.jpg)
What is the probability of observing one or more security violations, when the daily probability of violations is .01 and we are monitoring the organization for 4 months.
Do One
![Page 51: DISCRETE PROBABILITY DISTRIBUTIONS Farrokh Alemi Ph.D.](https://reader033.fdocuments.in/reader033/viewer/2022052402/56649dce5503460f94ac2b07/html5/thumbnails/51.jpg)
How many visits will it take to have at least one medication error if the estimated probability of medication error in a visit is 0.03?
Do Another