Discrete Probability Distributions : Discrete Probability Distributions Farrokh Alemi Ph.D.
Discrete Probability Distributions: Bernoulli Geometric Binomial Poisson Discrete Probability Distributions
Definitions: Density function Definitions
Definitions: Cumulative probability function Definitions
Definitions: Definitions
Expected Value: Expected Value
Expected Value: Expected Value
Expected Value: Expected Value
Expected Value: Expected Value
Example: Example
Example: Example
Example: Example
Example: Example
Example: Example
Example: Example
Density & Cumulative Distributions: Density & Cumulative Distributions
Typical Probability Density Functions: Bernoulli Geometric Binomial Poisson Typical Probability Density Functions
Bernoulli Probability Density Function: Mutually exclusive Bernoulli Probability Density Function
Bernoulli Probability Density Function: Exhaustive Bernoulli Probability Density Function
Bernoulli Probability Density Function: Bernoulli Probability Density Function
Bernoulli Probability Density Function: Bernoulli Probability Density Function
Independent Bernoulli Trials: Independent Bernoulli Trials
Independent Bernoulli Trials: Independent Bernoulli Trials
Geometric Density Function: Geometric Density Function
Geometric Density Function: Geometric Density Function
Geometric Density Function: Geometric Density Function
Do One: No medication errors have occurred in the past 90 days. What is the maximum daily probability of medication error in our facility? Do One
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
Binomial Probability Distribution: 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
Independent Bernoulli Trials: Independent Bernoulli Trials
Independent Bernoulli Trials: Independent Bernoulli Trials P x (1-P) x P
Binominal Probability Distribution: Different combinations Success probabilities Failure probabilities Binominal Probability Distribution
Binomial Probability Distribution: Binomial Probability Distribution
Binomial 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=1/2: 6 Trials of Binomial p=1/2
6 Trials of Binomial p=0.05: 6 Trials of Binomial p=0.05
Example: If the monthly probability of elopement is 0.05, how many patients will elope in 2 years? Example
Example: If the monthly probability of elopement is 0.05, how many patients will elope in 2 years? Example
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
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
Do One: 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
Poisson Density Function: Large number of trials Small probabilities of occurrence Poisson Density Function
Poisson Density Function: Poisson Density Function
Poisson Density Function: Poisson Density Function
Take Home Lesson: Repeated independent Bernoulli trials is the foundation of many distributions Take Home Lesson
Do One: 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
Do Another: 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