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  • Binomial, Poisson, and Multinomial Distributions
    COURSE INTRODUCTION
    Course Syllabus
    Unit 1: Statistics and Data
    1.1.1: What is Statistics?
    What are Statistics?
    1.1.2: Descriptive and Inferential Statistics
    Descriptive and Inferential Statistics
    Basic Definitions and Concepts
    1.1.3: Types of Data and Their Collection
    Variables and Data Collection
    Presenting Data
    1.2.1: Graphical Methods for Describing Quantitative Data
    Graphing
    Three Popular Data Displays
    1.2.2: Numerical Measures of Central Tendency and Variability
    Numerical Measures of Central Tendency and Variability
    Measures of Central Location
    Mean, Median, Mode, and Variance
    1.2.3: Methods for Describing Relative Standing
    Percentiles
    1.2.4: Methods for Describing Bivariate Relationships
    Scatterplots and Bivariate Data
    Pearson's r
    Unit 1 Assessment
    Unit 1 Assessment
    Unit 2: Elements of Probability and Random Variables
    2.1.1: Events, Sample Spaces, and Probability
    Introduction to Probability
    Basic Concepts of Probability
    2.1.2: Counting Rules
    Permutations and Combinations
    The Addition Rule for Probability with a Venn Diagram Example
    2.2.1: Common Discrete Random Variables
    Random Variables and Probability Distributions
    Binomial Distributions
    Binomial, Poisson, and Multinomial Distributions
    2.2.2: Normal Distribution
    The Standard Normal Distribution
    More on Normal Distributions
    Introduction to the Normal Distribution
    Unit 2 Assessment
    Unit 2 Assessment
    Unit 3: Sampling Distributions
    3.1.1: Continuous Random Variables
    Continuous Random Variables
    3.1.2: Definition and Interpretation
    Introduction to Sampling Distributions
    3.1.3: Sampling Distributions Properties
    Wolfram Demonstrations Project
    3.2.1: The Sampling Distribution of Sample Mean
    The Sampling Distribution of a Sample Mean
    The Mean, Standard Deviation, and Sampling Distribution of the Sample Mean
    Sampling Distribution
    3.2.2: The Sampling Distribution of Pearson's r
    Sampling Distribution of r
    3.2.3: The Sampling Distribution of the Sample Proportion
    Sampling Distribution of p
    Standard Deviation
    Unit 3 Assessment
    Unit 3 Assessment
    Unit 4: Estimation with Confidence Intervals
    4.1.1: Sample Statistics and Parameters
    Basic Sample Statistics and Parameters
    4.1.2: Bias and Sampling Variability
    Characteristics of Estimators
    4.2.1: Confidence Intervals for Mean
    Confidence Intervals for the Mean
    Demonstration: Confidence Intervals for a Mean
    t Distribution Demonstration
    Comparing Normal and Student's t-Distributions
    4.2.2: Confidence Intervals for Correlation and Proportion
    Confidence Intervals for Correlation and Proportion
    Confidence Intervals
    Unit 4 Assessment
    Unit 4 Assessment
    Unit 5: Hypothesis Test
    5.1.1: Setting up Hypotheses
    Setting Up Hypotheses
    5.1.2: Interpreting Hypotheses Testing Results
    The Observed Significance of a Test
    Results
    Hypothesis Testing with One Sample
    More on Hypothesis Testing
    5.1.3: Steps in Hypothesis Testing and Its Relation to Confidence Intervals
    Steps and Confidence Intervals in Hypothesis Testing
    5.2.1: Testing Single Mean
    Testing a Single Mean
    Sample Tests for a Population Mean
    5.2.2: Testing the Difference between Two Means
    The Difference between Two Means
    Difference of Means
    5.3: Chi-Square Distribution
    Contingency Tables
    Chi-Square Distributions and Goodness of Fit
    More on Chi-square Distributions
    5.4: Comparing the Proportions of Populations
    Comparing Population Proportions
    Unit 5 Assessment
    Unit 5 Assessment
    Unit 6: Linear Regression
    6.1.1: Scatter Plot of Two Variables and Regression Line
    Introduction to Linear Regression
    Linear Regression
    6.1.2: Correlation Coefficient
    Correlation
    The Linear Correlation Coefficient
    6.1.3: Sums of Squares
    Partitioning Sums of Squares
    Regression Lines
    6.2.1: Standard Errors of the Least Squares Estimates
    Standard Error of the Estimate
    6.2.2: Statistical Inference for the Slope and Correlation
    Inferential Statistics for b and r
    Statistical Inference about Slope
    6.2.3: Influential Observations
    Influential Observations
    A Complete Example
    6.3: ANOVA
    ANOVA
    More on ANOVA
    Unit 6 Assessment
    Unit 6 Assessment
    Study Guide
    MA121 Study Guide
    Course Feedback Survey
    Course Feedback Survey
    Certificate Final Exam
    MA121: Certificate Final Exam
    Archived Materials
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  • Computer Science
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Table of contents

  • Binomial Distribution
    • The Formula for Binomial Probabilities
    • Cumulative Probabilities
    • Mean and Standard Deviation of Binomial Distributions
    • Video
    • Questions
    • Answers
  • Poisson Distribution
    • Video
    • Question
    • Answer
  • Multinomial Distribution
    • Question
    • Answer
  1. MA121: Introduction to Statistics
  2. Unit 2: Elements of Probability and Random Variables
  3. 2.2: Random Variables and Distributions
  4. 2.2.1: Common Discrete Random Variables
  5. Binomial, Poisson, and Multinomial Distributions

Binomial, Poisson, and Multinomial Distributions

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First, we will talk about binomial probabilities, how to compute their cumulatives, and the mean and standard deviation. Then, we will introduce the Poisson probability formula, define multinomial outcomes, and discuss how to compute probabilities by using the multinomial distribution.

 

https://onlinestatbook.com/movies/probability/poisson.mp4
 

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Saylor Academy © 2010-2025 except as otherwise noted. Excluding course final exams, content authored by Saylor Academy is available under a Creative Commons Attribution 3.0 Unported license. Third-party materials are the copyright of their respective owners and shared under various licenses. See detailed licensing information. Saylor Academy®, Saylor.org®, and Harnessing Technology to Make Education Free® are trade names of the Constitution Foundation, a 501(c)(3) organization through which our educational activities are conducted.