Hypergeometric Distribution
"In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of 
In statistics, the hypergeometric test uses the hypergeometric distribution to calculate the statistical significance of having drawn a specific
Binomial Distribution
"In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own boolean-valued outcome: success/yes/true/one (with probability p) or failure/no/false/zero (with probability q = 1 − p). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment and a sequence of outcomes is called a Bernoulli process; for a single trial, i.e., n = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance.
The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric distribution, not a binomial one. However, for N much larger than n, the binomial distribution remains a good approximation, and is widely used."
https://en.wikipedia.org/wiki/Binomial_distribution
Negative Binomial Distribution
"In probability theory and statistics, the negative binomial distribution is a discrete probability distribution of the number of successes in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of failures (denoted r) occurs. For example, we can define that when we throw a dice and get a 6 it is a failure while rolling any other number is considered a success, and also choose r to be 3. We then throw the dice repeatedly until the third time the number 6 appears. In such a case, the probability distribution of the number of non-6s that appeared will be a negative binomial distribution.
The Pascal distribution (after Blaise Pascal) and Polya distribution (for George Pólya) are special cases of the negative binomial distribution. A convention among engineers, climatologists, and others is to use "negative binomial" or "Pascal" for the case of an integer-valued stopping-time parameter r, and use "Polya" for the real-valued case."
https://en.wikipedia.org/wiki/Negative_binomial_distribution
Probability and Counting
"To decide "how likely" an event is, we need to count the number of times an event could occur and compare it to the total number of possible events. Such a comparison is called the probability of the particular event occurring. The mathematical theory of counting is known as combinatorial analysis"
https://www.intmath.com/counting-probability/counting-probability-intro.php
Principle of Counting
"The Fundamental Counting Principle (also called the counting rule) is a way to figure out the number of outcomes in a probability problem. Basically, you multiply the events together to get the total number of outcomes. The formula is:
If you have an event “a” and another event “b” then all the different outcomes for the events is a * b."
https://www.statisticshowto.datasciencecentral.com/fundamental-counting-principle/
Combinatorics
https://mathigon.org/world/Combinatorics
fundamental principle of counting
"The Fundamental Counting Principle states that if one event has m possible outcomes and a second independent event has n possible outcomes, then there are m x n total possible outcomes for the two events together."
https://www.mathgoodies.com/glossary/term/Fundamental%20Counting%20Principle
Factorial
"In mathematics, the factorial of a positive integer n, denoted by n!, is the product of all positive integers less than or equal to n:
{\displaystyle n!=n\times (n-1)\times (n-2)\times (n-3)\times \cdots \times 3\times 2\times 1\,.}
https://en.wikipedia.org/wiki/Factorial
Factorial with Identical Numbers
"Bayes' theorem
Description
In probability theory and statistics, Bayes’s theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event. Wikipedia
Formula
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= | events |
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= | probability of A given B is true |
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= | probability of B given A is true |
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= | the independent probabilities of A and B |
"
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Note: Older short-notes from this site are posted on Medium: https://medium.com/@SayedAhmedCanada
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Sayed Ahmed
BSc. Eng. in Comp. Sc. & Eng. (BUET)
MSc. in Comp. Sc. (U of Manitoba, Canada)
MSc. in Data Science and Analytics (Ryerson University, Canada)
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