**Discrete Probability Distributions**

## Presentation Description

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

##
Comments

##
Presentation Transcript

### Probability Distributions for Discrete Variables:

Probability Distributions for Discrete Variables 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 for variable x### Expected Value:

Expected Value Probability of event “i”### Expected Value:

Expected Value Value of event “i”### Expected Value:

Expected Value Summed over all possible events### Example:

Example### Example:

Example### Example:

Example Expected medication errors### Example:

Example### Example:

Example### Example:

Example### Density & Cumulative Distributions:

Density & Cumulative Distributions### Typical Probability Density Functions:

Bernoulli Binomial Geometric 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:

Independence = H istory does not matter Independent Bernoulli Trials### Independent Bernoulli Trials:

Independent Bernoulli Trials Patient elopes No event Patient elopes No event Patient elopes No event Month 1 Month 2 Month 3### Geometric Density Function:

Geometric Density Function K-1 non-occurrence of the event occurrence of the event### 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 Month### Independent Bernoulli Trials:

Independent Bernoulli Trials Month (1-P) x P x P### Independent Bernoulli Trials:

Independent Bernoulli Trials Month (1-P) x P x P### 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 n! is n factorial and is calculated as 1*2*3*…*n Possible ways of getting k occurrences in n trials### Binomial Probability Distribution:

Binomial Probability Distribution k occurrences of the event### Binomial Probability Distribution:

Binomial Probability Distribution n-k non-occurrence of the event### 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 The expected value of a Binomial distribution is np . The variance is np (1-p)### 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 Expected number of trials, np### Poisson Density Function:

Poisson Density Function k is number of sentinel occurrences### 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## View More Presentations

## Tags Add Tags

## Presentation Statistics

loading.....## Channel Statistics

Included in these Channels: