Discrete Probability Distributions

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This is part of open online course on managerial statistics. This lecture is on discrete distributions. The complete course and other videos are available at http://openonlinecourses.com/statistics

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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