THE POISSON DISTRIBUTION Section 6 3 Copyright 2016

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THE POISSON DISTRIBUTION Section 6. 3 Copyright © 2016 The Mc. Graw-Hill Companies, Inc.

THE POISSON DISTRIBUTION Section 6. 3 Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Objectives 1. 2. 3. Compute probabilities for Poisson random variables Compute the mean, variance,

Objectives 1. 2. 3. Compute probabilities for Poisson random variables Compute the mean, variance, and standard deviation of a Poisson random variable Use the Poisson distribution to approximate binomial probabilities Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

OBJECTIVE 1 Compute probabilities for Poisson random variables (Hand Computation) Copyright © 2016 The

OBJECTIVE 1 Compute probabilities for Poisson random variables (Hand Computation) Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Poisson Distribution Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction

Poisson Distribution Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Poisson Distribution Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction

Poisson Distribution Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Example – Poisson Distribution Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required

Example – Poisson Distribution Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Probabilities for the Poisson Distribution Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission

Probabilities for the Poisson Distribution Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Example – Poisson Probabilities Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required

Example – Poisson Probabilities Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Application of Poisson Distribution Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required

Application of Poisson Distribution Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

OBJECTIVE 1 Compute probabilities for Poisson random variables (TI-83 PLUS) Copyright © 2016 The

OBJECTIVE 1 Compute probabilities for Poisson random variables (TI-83 PLUS) Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Poisson Distribution Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction

Poisson Distribution Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Poisson Distribution Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction

Poisson Distribution Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Example – Poisson Distribution Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required

Example – Poisson Distribution Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Probabilities for the Poisson Distribution Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission

Probabilities for the Poisson Distribution Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Poisson Probabilities on the TI-84 PLUS Copyright © 2016 The Mc. Graw-Hill Companies, Inc.

Poisson Probabilities on the TI-84 PLUS Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Example – Poisson Probabilities Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required

Example – Poisson Probabilities Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Application of Poisson Distribution Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required

Application of Poisson Distribution Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

OBJECTIVE 2 Compute the mean, variance, and standard deviation of a Poisson random variable

OBJECTIVE 2 Compute the mean, variance, and standard deviation of a Poisson random variable Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Poisson – Mean, Variance, & Standard Deviation Copyright © 2016 The Mc. Graw-Hill Companies,

Poisson – Mean, Variance, & Standard Deviation Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

OBJECTIVE 3 Use the Poisson distribution to approximate binomial probabilities Copyright © 2016 The

OBJECTIVE 3 Use the Poisson distribution to approximate binomial probabilities Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Approximating the Binomial Distribution Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required

Approximating the Binomial Distribution Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

Example – Poisson Approximation Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required

Example – Poisson Approximation Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

You Should Know… • • How to tell if a random variable has a

You Should Know… • • How to tell if a random variable has a Poisson Distribution How to compute probabilities for Poisson random variables How to compute the mean, variance, and standard deviation of a Poisson random variable How to use the Poisson distribution to approximate binomial probabilities Copyright © 2016 The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

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Standard deviation formula for poisson distribution

Standard deviation formula for poisson distribution

Poisson distribution on ti 84

Poisson distribution on ti 84

Example of poisson distribution

Example of poisson distribution

Geometric distribution conditions

Geometric distribution conditions

Poisson process examples and solutions

Poisson process examples and solutions

Poisson distrubution

Poisson distrubution

Poisson distribution football

Poisson distribution football

Poisson distribution conditions

Poisson distribution conditions

Binomial distribution moment generating function

Binomial distribution moment generating function

Poisson distribution notation

Poisson distribution notation

Exponential

Discrete probability formula

Discrete probability formula

Poisson distribution table

Poisson distribution table

Pbinomial

Poisson distribution notation

Poisson distribution notation

Poisson and geometric distribution

Poisson and geometric distribution

Derived distributions

Derived distributions

Standard deviation formula for poisson distribution

Standard deviation formula for poisson distribution

Probability mass function of poisson distribution

Probability mass function of poisson distribution

Hypergeometric distribution definition

Hypergeometric distribution definition

Binomial distrubution

Binomial distrubution

Poisson distribution examples

Poisson distribution examples

Uniform distribution formula

Uniform distribution formula

Characteristics of poisson distribution

Characteristics of poisson distribution

Distribucin Poisson Distribucin Poisson Definicin La distribucin Poisson

Distribucin Poisson Distribucin Poisson Definicin La distribucin Poisson

POISSON DISTRIBUTIONS POISSON POISSON 1781 1840 DEFINITION The

POISSON DISTRIBUTIONS POISSON POISSON 1781 1840 DEFINITION The

The Poisson Probability Distribution The Poisson probability distribution

The Poisson Probability Distribution The Poisson probability distribution

Poisson Distribution Gauss Distribution Origin Adj RSquare Poisson

Poisson Distribution Gauss Distribution Origin Adj RSquare Poisson

POISSON DISTRIBUTION INTRODUCTION Poisson distribution is a discrete

POISSON DISTRIBUTION INTRODUCTION Poisson distribution is a discrete

ii Poisson distribution The Poisson distribution resembles the

ii Poisson distribution The Poisson distribution resembles the

Poisson Distribution ABUBAKR SAEED 15700293 Poisson Distribution It

Poisson Distribution ABUBAKR SAEED 15700293 Poisson Distribution It

Poisson Distribution s Definition The Poisson Distribution occurs

Poisson Distribution s Definition The Poisson Distribution occurs

POISSON DISTRIBUTION Poisson distribution may be expected in

POISSON DISTRIBUTION Poisson distribution may be expected in

Subject probability statistics Topic Poisson Distribution Poisson Distribution

Subject probability statistics Topic Poisson Distribution Poisson Distribution

PROBABILITY DISTRIBUTION BINOMIAL POISSON NORMAL BINOMIAL AND POISSON

PROBABILITY DISTRIBUTION BINOMIAL POISSON NORMAL BINOMIAL AND POISSON

Y Dosraniad Poisson The Poisson Distribution Maer Dosraniad

Y Dosraniad Poisson The Poisson Distribution Maer Dosraniad

THE POISSON DISTRIBUTION The Poisson random variable was

THE POISSON DISTRIBUTION The Poisson random variable was

Exponential and Poisson Chapter 5 Material Poisson Distribution

Exponential and Poisson Chapter 5 Material Poisson Distribution

The Poisson Distribution We can use the Poisson

The Poisson Distribution We can use the Poisson

Geometric Distribution Poisson Distribution Week 8 Geometric Distribution

Geometric Distribution Poisson Distribution Week 8 Geometric Distribution

2 Probability Distribution Binomial Distribution Poisson Distribution 20201124

2 Probability Distribution Binomial Distribution Poisson Distribution 20201124

Probability Distribution Binomial Distribution Poisson Distribution l HHH

Probability Distribution Binomial Distribution Poisson Distribution l HHH

SECTION 5 5 POISSON PROBABILITY DISTRIBUTIONS POISSON DISTRUBUTION

SECTION 5 5 POISSON PROBABILITY DISTRIBUTIONS POISSON DISTRUBUTION

SECTION 5 5 POISSON PROBABILITY DISTRIBUTIONS POISSON DISTRUBUTION

SECTION 5 5 POISSON PROBABILITY DISTRIBUTIONS POISSON DISTRUBUTION

DISTRIBUSI POISSON DAN HIPERGEOMETRIK SEJARAH DISTRIBUSI POISSON Distribusi

DISTRIBUSI POISSON DAN HIPERGEOMETRIK SEJARAH DISTRIBUSI POISSON Distribusi

Distribucin de Poisson Simon Denis Poisson 1781 1840

Distribucin de Poisson Simon Denis Poisson 1781 1840