Introduction to Discrete & Continuous Probability Distributions

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  ✅ 1. What is a Probability Distribution? A probability distribution describes how probabilities are distributed over the values of a random variable . Random Variable : A variable whose values are outcomes of a random phenomenon. ๐Ÿงฎ 2. Types of Probability Distributions Type Description GIS Example Discrete           Takes countable values  Number of landslides per year in a          valley Continuous          Takes infinite values over an                 interval Rainfall (mm), elevation, temperature  ๐Ÿ“Œ Discrete Probability Distributions ๐ŸŽฏ 3. Binomial Distribution ✅ Definition : Used when an experiment is repeated n times , and each trial has two outcomes : success or failure. ✅ Conditions : Fixed number of trials (n) Only two possible outcomes per trial (success/failure) Constant probability of success (p) Trials are in...
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Introduction to Probability

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✅ 1. What is Probability?

  • Definition: Probability is the numerical measure of the likelihood that a particular event will happen.

  • Relevance to GIS: Helps in risk mapping, spatial modeling, disaster prediction, land-use forecasting, and uncertainty analysis in geospatial data.


๐Ÿง  2. Key Concepts and Terminology

TermDescriptionGIS Example
ExperimentA process that generates dataMapping landslide zones in a valley
Sample Space (S)All possible outcomes{High risk, Medium risk, Low risk} zones
Event (E)Specific outcome or a group of outcomesE: “Zone is high risk”


๐Ÿ”ข 3. Basic Probability Formula

P(E)=Number of favorable outcomesTotal number of outcomesP(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}

๐Ÿ“ Example:
You analyze 100 buildings in a flood-prone area. 25 buildings are in high-risk zones.

P(High-risk building)=25100=0.25

P(\text{High-risk building}) = \frac{25}{100} = 0.25


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