Andrew Gurung
  • Introduction
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    • Linear Algebra
      • Linear algebra explained in four pages
      • Vectors
        • Vector Basics
        • Vector Projection
        • Cosine Similarity
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        • Linear combination and span
        • Linear independence and Basis vectors
      • Matrices
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        • Matrix types
      • Eigendecomposition, Eigenvectors and Eigenvalues
      • Principle Component Analysis (PCA)
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      • Linear Algebra: Deep Learning Book
    • Calculus
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      • Scalar Derivative and Partial Derivatives
      • Gradient
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      • Maxima and Minima using Derivatives
      • Gradient Descent and its types
    • Statistics and Probability
      • Probability Rules and Axioms
      • Types of Events
      • Frequentist vs Bayesian View
      • Random Variables
      • MLE, MAP, and Naive Bayes
      • Probability Distributions
      • P-Value and hypothesis test
    • 7 Step DS Process
      • 1: Business Requirement
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      • 3: Data Processing
        • SQL Techniques
        • Cleaning Text Data
      • 4: Data Exploration
      • 5: Modeling
      • 6: Model deployment
      • 7: Communication
    • Miscellaneous
      • LaTeX commands
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    • Primer
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      • Aristotle's Defense of Private Property
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  • Important terms
  • Probability Rules
  • Probability Axioms

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  1. Data Science
  2. Statistics and Probability

Probability Rules and Axioms

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Last updated 6 years ago

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Probability is a way to quantify the uncertainty that arises from conducting experiments using a random sample from the population of interest. Probability of an event happening = (Number of ways it can happen) / (Total number of outcomes)

Example: the chances of rolling a '3' with a die Number of ways it can happen: 1 Total number of outcomes: 6 So the Probability = 1/6

Important terms

Sample Space: all the possible outcomes of an experiment Sample Point: just one of the possible outcomes Event: one or more outcomes of an experiment

Example: the chances of a "double" when rolling 2 dice. Sample Space: Possible outcomes. 36 sample points {1,1} {1,2} {1,3} {1,4} ... {6,3} {6,4} {6,5} {6,6}

Event: Looking for double. Event is made up of 6 sample points. {1,1} {2,2} {3,3} {4,4} {5,5} and {6,6} Run 100 Experiments, and find how many Events you observe.

Probability Rules

Probability Rule One: For any event A, 0 ≤ P(A) ≤ 1 Probability Rule Two: The sum of the probabilities of all possible outcomes is 1. Probability Rule Three: P(not A) = 1 – P(A) Probability Rule Four: If A and B are disjoint events, then P(A or B) = P(A) + P(B)

Probability Axioms

Axiom One: The probability of an event is a non-negative real number that is greater than or equal to 0. Axiom Two: The probability of the entire sample space is one(no events exist outside of the sample space) Axiom Three: If two events A and B are mutually exclusive, then the probability of either A or B [i.e P(A U B)] = P(A) + P(B)

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Probability
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Basic Probability Rules