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...

Requirement of a good sample

 

A good sample is one that is representative of the population from which it is drawn. This means that the sample should have the same characteristics as the population in terms of important variables such as age, gender, race, ethnicity, income, education level, and so on.

There are a number of requirements for a good sample, including:

  • Accuracy: The sample should be an accurate representation of the population. This means that the sample results should be generalizable to the population as a whole.
  • Precision: The sample should be precise, meaning that the results of the sample should be consistent from one sample to another.
  • Reliability: The sample should be reliable, meaning that the results of the sample can be reproduced over time.
  • Unbiasedness: The sample should be unbiased, meaning that the results of the sample are not influenced by any systematic errors.


In addition to these general requirements, there are a number of specific requirements for a good sample, depending on the type of research being conducted. For example, a sample for a clinical trial may need to be stratified by age, gender, and other important factors.

Here are some tips for ensuring that your sample is representative of the population:

  • Use a probability sampling method, such as simple random sampling, stratified sampling, or cluster sampling.
  • Use a large enough sample size. The larger the sample size, the more representative the sample is likely to be of the population.
  • Select your sample from a variety of sources. This will help to ensure that your sample is not biased towards any particular group of people.


Once you have collected your sample, you should check to make sure that it is representative of the population in terms of important variables. You can do this by comparing the sample characteristics to the population characteristics. If the sample characteristics are similar to the population characteristics, then you can be confident that your sample is representative of the population.

Here are some examples of how to check whether your sample is representative of the population:

  • If you are sampling from a student population, you could compare the age, gender, and race distribution of your sample to the age, gender, and race distribution of the student population as a whole.
  • If you are sampling from a consumer population, you could compare the age, gender, income, and education level distribution of your sample to the age, gender, income, and education level distribution of the consumer population as a whole.

If you find that your sample is not representative of the population in terms of important variables, you may need to collect a new sample

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