discrete probability distributions farrokh alemi ph.d
TRANSCRIPT
DISCRETE PROBABILITY DISTRIBUTIONS
Farrokh Alemi Ph.D.
BernoulliGeometricBinomialPoisson
Discrete Probability Distributions
Density function
Definitions
Cumulative probability function
Definitions
Definitions
Expected Value
Expected Value
Expected Value
Expected Value
Example
Example
Example
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
Example
Example
Density & Cumulative Distributions
BernoulliGeometricBinomialPoisson
Typical Probability Density Functions
Mutually exclusive
Bernoulli Probability Density Function
Exhaustive
Bernoulli Probability Density Function
Bernoulli Probability Density Function
pOccurs
1-PDoes not occur
Probability density functionEvents
pOccurs
1-PDoes not occur
Probability density functionEvents
Bernoulli Probability Density Function
Independent Bernoulli Trials
Independent Bernoulli Trials
Geometric Density Function
Geometric Density Function
Geometric Density Function
No medication errors have occurred in the past 90 days. What is the maximum daily probability of medication error in our facility?
Do One
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
Number of k occurrences of the event in n independent trials
Binomial Probability Distribution
Independent Bernoulli Trials
Independent Bernoulli Trials
Independent Bernoulli Trials
Independent Bernoulli Trials
P x (1-P) x P
Different combinationsSuccess probabilitiesFailure probabilities
Binominal Probability Distribution
Binomial Probability Distribution
Binomial Probability Distribution
Binomial Probability Distribution
6 Trials of Binomial p=1/2
6 Trials of Binomial p=1/2
6 Trials of Binomial p=0.05
If the monthly probability of elopement is 0.05, how many patients will elope in 2 years?
Example
If the monthly probability of elopement is 0.05, how many patients will elope in 2 years?
Example
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
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
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
Large number of trialsSmall probabilities of occurrence
Poisson Density Function
Poisson Density Function
k
Poisson Density Function
k
Repeated independent Bernoulli trials is the foundation of many distributions
Take Home Lesson
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
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