Probability Collection Book

DavidK, 23.10.2020

Introducing Probability in a Statistics Course

Inhaltsverzeichnis

  1. Probability Terminology and Notation
    1. Experimental Definitions
    2. Two Examples
  2. Finding Probability of an Event
    1. Classical Method to Determine Probability
    2. Doubles or Evens?
    3. Empirical Method
    4. The Law of Large Numbers
    5. Compliment Probability
    6. Empirical Method. Law of Large Numbers
  3. Mutually Exclusive, Joint Probability, Independent
    1. Mutually Exclusive Events and the Addition Rule
    2. Joint Probability Tables
    3. Medical Tests: Sensitivity, Specificity, etc
  4. Probability Simulations
    1. Probability of Suited Hands
    2. Random Integer Generator
    3. Dice Rolling Simulation
  5. Probability Formulas
    1. Calculating Mean, Standard Deviation, 5-number Summary, IQR
    2. Chi Squared Goodness of Fit Flipping 1 Coin
  6. Statistics
    1. Poisson Probability Simulation
    2. the bell curve
    3. Z Scores and Quantiles
    4. AQR Section 18: Sample Mean and Sample Standard Deviation
    5. The Sampling Distribution
  7. Definition of joint probability function
    1. Joint Probability function
  8. Marginal probability function of X and Y :g(x) and h(y)
    1. Marginal Probability Calculator_Continuous Case only
  9. Expected Value of X. Y : E(X.Y)
  10. Venn Diagrams and Conditional Probability
    1. Venn Diagrams using Set Notation & Words
    2. Shading Venn Diagrams
    3. Venn Diagrams and Notation
    4. Tree Diagrams and Venn Diagrams
    5. Word Problem connected to Venn Diagrams
  11. Probability & Intro. to Stat.
    1. Randomly Flip a Coin
    2. Roll Die Simulation
    3. Dice
    4. Randomly Pick Letter in Alphabet & Replace
    5. Randomly Pick a Card and Replace
    6. Spinner Six Sections (1 grey, 2 black, 3 white)
    7. Spinner (2 to 12 sections) V1
    8. Simulation of Sum of Dice
    9. Simulated Sums of Dice
    10. Probability
    11. Dice Roll Distribution
    12. BJD Probability Distribution Tool : Optional Input
    13. Boxplot Tool - Five Number Summary (0 to 200)
    14. Probability Dart Hits Triangle
    15. Random Darts Hit Triangle inside Square
    16. Chi Squared Goodness of Fit Flipping 1 Coin
    17. Normal Distribution: mean, std.dev.
    18. Standard Normal Curve
    19. Standard Normal Curve Calculator: z-scores
    20. One Son Policy
    21. AHA Compare Two Normal Curves
    22. AHE Compare Two Normal Curves 0<µ<5
    23. AHG Normal Distribution of MPG & Weekly Cost
    24. BJD Probability Distribution Tool
    25. 192 Normal Distribution Simulation : Bike & Wall
    26. BJH Simulation of a Poll Given Population Percent
    27. BAG Which Value of P Creates Greatest Sigma?
    28. BEE Confidence Interval Given M.E. & Sample Size
    29. 188 Inverse Normal Calculator
    30. TI84 Normalcdf Practice Scored
    31. Spinners (2 to 12 sections) V0 Instant
    32. z-Scores
    33. ME Given Sample Size: Sample Size Given ME
    34. 100 Trials of 100 Flips of a Fair Coin
    35. Compare Combinations & Permutations
    36. Calculate Grade for the Year
    37. FIT Data to Quadratic v1
    38. Task: Find Mean, Median, Range, Mean Absolute Deviation, Standard Deviation
    39. Number Line Data Set & Statistics on The Data
    40. Horse Race Handicapped

1.

Probability Terminology and Notation

Understand the statistical mean of [list] [*]experiment [*]event [*]outcome / simple event [/list] Use probability P notation.

  • 1. Experimental Definitions
  • 2. Two Examples

1.1.

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1.2.

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2.

Finding Probability of an Event

Use the classical method and empirical method to find probabilities. Explain and use the law of large numbers.

  • 1. Classical Method to Determine Probability
  • 2. Doubles or Evens?
  • 3. Empirical Method
  • 4. The Law of Large Numbers
  • 5. Compliment Probability
  • 6. Empirical Method. Law of Large Numbers

2.1.

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2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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3.

Mutually Exclusive, Joint Probability, Independent

Create a table for joint probabilities and determine whether events are mutually exlusive, overlapping, independent, and dependent. Learn the probability properties these events have.

  • 1. Mutually Exclusive Events and the Addition Rule
  • 2. Joint Probability Tables
  • 3. Medical Tests: Sensitivity, Specificity, etc

3.1.

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3.2.

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3.3.

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4.

Probability Simulations

  • 1. Probability of Suited Hands
  • 2. Random Integer Generator
  • 3. Dice Rolling Simulation

4.1.

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4.2.

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4.3.

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5.

Probability Formulas

  • 1. Calculating Mean, Standard Deviation, 5-number Summary, IQR
  • 2. Chi Squared Goodness of Fit Flipping 1 Coin

5.1.

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5.2.

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6.

Statistics

  • 1. Poisson Probability Simulation
  • 2. the bell curve
  • 3. Z Scores and Quantiles
  • 4. AQR Section 18: Sample Mean and Sample Standard Deviation
  • 5. The Sampling Distribution

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7.

Definition of joint probability function

यो GeoGebra worksheet ले दुईवटा continuous random variable X and Y को joint function मा हुने Total probability 1 छ वा छैन हिसाब गर्न सहयोग गर्ने छ ।

  • 1. Joint Probability function

7.1.

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8.

Marginal probability function of X and Y :g(x) and h(y)

यो GeoGebra Book ले दुईवटा continuous random variable X and Y को joint probability distribution मा हुने Marginal probability function हिसाब गर्न सहयोग गर्ने छ ।

  • 1. Marginal Probability Calculator_Continuous Case only

8.1.

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9.

Expected Value of X. Y : E(X.Y)


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10.

Venn Diagrams and Conditional Probability

  • 1. Venn Diagrams using Set Notation & Words
  • 2. Shading Venn Diagrams
  • 3. Venn Diagrams and Notation
  • 4. Tree Diagrams and Venn Diagrams
  • 5. Word Problem connected to Venn Diagrams

10.1.

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10.2.

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10.4.

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10.5.

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11.

Probability & Intro. to Stat.

Probability Simulations and Demonstrations

  • 1. Randomly Flip a Coin
  • 2. Roll Die Simulation
  • 3. Dice
  • 4. Randomly Pick Letter in Alphabet & Replace
  • 5. Randomly Pick a Card and Replace
  • 6. Spinner Six Sections (1 grey, 2 black, 3 white)
  • 7. Spinner (2 to 12 sections) V1
  • 8. Simulation of Sum of Dice
  • 9. Simulated Sums of Dice
  • 10. Probability
  • 11. Dice Roll Distribution
  • 12. BJD Probability Distribution Tool : Optional Input
  • 13. Boxplot Tool - Five Number Summary (0 to 200)
  • 14. Probability Dart Hits Triangle
  • 15. Random Darts Hit Triangle inside Square
  • 16. Chi Squared Goodness of Fit Flipping 1 Coin
  • 17. Normal Distribution: mean, std.dev.
  • 18. Standard Normal Curve
  • 19. Standard Normal Curve Calculator: z-scores
  • 20. One Son Policy
  • 21. AHA Compare Two Normal Curves
  • 22. AHE Compare Two Normal Curves 0<µ<5
  • 23. AHG Normal Distribution of MPG & Weekly Cost
  • 24. BJD Probability Distribution Tool
  • 25. 192 Normal Distribution Simulation : Bike & Wall
  • 26. BJH Simulation of a Poll Given Population Percent
  • 27. BAG Which Value of P Creates Greatest Sigma?
  • 28. BEE Confidence Interval Given M.E. & Sample Size
  • 29. 188 Inverse Normal Calculator
  • 30. TI84 Normalcdf Practice Scored
  • 31. Spinners (2 to 12 sections) V0 Instant
  • 32. z-Scores
  • 33. ME Given Sample Size: Sample Size Given ME
  • 34. 100 Trials of 100 Flips of a Fair Coin
  • 35. Compare Combinations & Permutations
  • 36. Calculate Grade for the Year
  • 37. FIT Data to Quadratic v1
  • 38. Task: Find Mean, Median, Range, Mean Absolute Deviation, Standard Deviation
  • 39. Number Line Data Set & Statistics on The Data
  • 40. Horse Race Handicapped

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