Maths A Level
Binomial Distributions

What is Binomial Distribution?

In Mendel’s experiment, you could observe any number of green peas. It’s possible to calculate the probability of finding each number. If you put all of those probabilities in one diagram, you get a special type of probability distribution, called binomial distribution.

 

Transcript

Lesson overview

Basic Probability Distributions

  1. Introduction to Probability Distributions
  2. The Things We Record
  3. Probability Tables
  4. Probability Bar Graphs
  5. Probability Distribution
  6. Uniform Distribution
  7. Different Experiment, Same Sample Space
  8. Probability Distribution Notation
  9. Probability Lists
  10. Probability Distribution Notation: The Outcomes
  11. Probability Distribution Notation: P(X = x)
  12. Piecewise Notation
  13. Probability Functions
  14. Completing the Probability Function
  15. Non-Numerical Outcomes
  16. Random Variables

Binomial Distributions

  1. Introduction to Binomial Distributions
  2. Binomial Trials
  3. Binomial Distributions
  4. Features of Binomial Distributions
  5. Setting Up a Binomial Expression
  6. )
  7. Finding Probabilities in a Binomial Distribution
  8. Our Old Friend the Calculator
  9. Bringing in the Random Variable
  10. When Can We Use Binomial Distributions?
  11. Independent Trials
  12. The Magic of Binomial Distributions
  13. Binomial Distribution Notation
  14. Changing the Probability of Success
  15. Changing the Number of Trials
  16. The Mendel-Fisher Controversy

Cumulative Distributions

  1. Introduction to Cumulative Distributions
  2. The Manual Approach
  3. Cumulative Distributions
  4. Plotting Cumulative Distributions
  5. Other Cumulative Distributions
  6. Finding Cumulative Probabilities With Your Calculator
  7. Finding P(X<x)
  8. Finding P(X>x)
  9. Finding P(X≥x)
  10. Working Backwards
  11. Gombaud’s Game

Continuous Random Variables

  1. Introduction to Continuous Random Variables
  2. Continuous Random Variables
  3. Discrete Does Not Mean Finite
  4. A Problem With Continuous Random Variables
  5. Ranges of Outcomes
  6. Finding Probabilities With Histograms
  7. Probability Histograms
  8. Supercharging Histograms With Curves
  9. Representing Probability With Height vs Area

Normal Distributions

  1. Introduction to Normal Distributions
  2. A Normal Distribution
  3. Mean and Standard Deviation
  4. Varying the Standard Deviation
  5. The Asymptote of the Normal Distribution
  6. Normal Distribution Probability Zones – Part 1
  7. Equal To or Not Equal To
  8. Normal Distribution Probability Zones – Part 2
  9. Calculating Probabilities – Part 1
  10. Calculating Probabilities – Part 2
  11. The Four Question Types
  12. Relating areas under a normal curve
  13. Inverse Problems
  14. Normal Distribution Notation
  15. Variance and the Standard Deviation
  16. The Standard Normal Distribution
  17. Finding the Mean
  18. Finding the Standard Deviation
  19. Using Phi

A Normal Model for Binomial Distributions

  1. Introduction to a Normal Model for Binomial Distributions
  2. When Binomial Distributions Behave Normally
  3. Limitations of Normal Approximations
  4. The Continuity Correction
  5. Finding the Mean of the Normal Approximation
  6. Finding the Variance of the Normal Approximation

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