Introduction to Discrete & Continuous Probability Distributions

  ✅ 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...

Probability Sampling Techniques

 

Probability Sampling Techniques

Probability sampling techniques are methods that allow researchers to select a sample from a population using random selection. These techniques provide every individual in the population with a known, non-zero probability of being included in the sample. Here are some commonly used types of probability sampling techniques:

  1. Simple Random Sampling:

Simple random sampling is a basic form of probability sampling where each individual in the population has an equal chance of being selected. This is typically done using a random number generator or a table of random numbers.

  1. Stratified Sampling:

Stratified sampling involves dividing the population into distinct subgroups or strata based on certain characteristics that are relevant to the research objective (e.g., age, gender, income). A random sample is then taken from each stratum proportionate to its size, ensuring representation from all subgroups.



  1. Cluster Sampling:

Cluster sampling involves dividing the population into clusters or groups. Clusters are formed based on some natural grouping (e.g., geographical location, schools, households). A random sample of clusters is selected, and all individuals within the selected clusters are included in the sample.

  1. Systematic Sampling:

Systematic sampling involves selecting individuals from the population at regular intervals, using a random starting point. For example, if the population size is N and the desired sample size is n, every N/nth individual is selected. This technique is simple to implement and provides a representative sample if the population has no systematic ordering.

  1. Probability Proportional to Size Sampling:

In this technique, the probability of selection is directly proportional to the size or importance of each unit in the population. Larger units have a higher probability of being included in the sample. This method is useful when the size of units varies widely across the population.

  1. Multi-stage Sampling:

Multi-stage sampling involves a combination of sampling techniques. It is often used when the population is large and geographically dispersed. The population is divided into clusters, and then a random sample of clusters is selected. Within each selected cluster, further sampling is conducted using techniques like simple random sampling or systematic sampling.

  1. Double Sampling:

 Double sampling involves initially selecting a smaller sample from the population, followed by a more detailed or thorough selection of individuals from within that sample. It allows researchers to conduct an initial assessment or screening before selecting a more focused sample.

These probability sampling techniques help ensure that the sample selected is representative of the population, increasing the generalizability and reliability of the research findings. The choice of technique depends on the characteristics of the population, research objectives, available resources, and practical considerations.

 

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