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Types of Probability

Bernoulli and Uniform
Bernoulli and Uniform

In probability theory and statistics, the Bernoulli distribution, named after Swiss scientist Jacob Bernoulli,[1] is the probability distribution of a random variable which takes the value 1 with probability p {\displaystyle p} and the value 0 with probability q = 1 − p {\displaystyle q=1-p} — i.e., the probability distribution of any single ...

Binomial and Hypergeometric
Binomial and Hypergeometric

Contents of this Probability theory tutorial: Random variable, Binomial distribution, Hypergeometric distribution, Poisson distribution, Probability, Average, Random variable with limit, Random variable without limit, Expected value, Standard deviation.

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Cluster Sampling
Cluster Sampling

Cluster sampling involves identification of cluster of participants representing the population and their inclusion in the sample group. This is a popular method in conducting marketing researches. The main aim of cluster sampling can be specified as cost reduction and increasing the levels of efficiency of sampling.

Exponential and Weibull
Exponential and Weibull

Relation between Weibull and exponential distributions. up vote 1 down vote favorite. 1. The probability distribution function of a Weibull distribution is as follows: f(x)=a⋅b−axa−1⋅e(−x/b)a,x>0 for parameters a,b>0. I have to show that X∼Weibull(a,b) iff Xa∼expo(ba).

image: itl.nist.gov
Gamma and Beta
Gamma and Beta

This concerns the relationship between the Gamma and Beta distributions as opposed to the Gamma and Beta functions. Let $X \sim \mbox{Gamma}(\alpha, 1)$ and $Y \sim \mbox{Gamma}(\beta, 1)$ where the paramaterization is such that $\alpha$ is the shape parameter.

Geometric and Negative Binomial
Geometric and Negative Binomial

Geometric Distribution. The geometric distribution is a special case of the negative binomial distribution. It deals with the number of trials required for a single success. Thus, the geometric distribution is negative binomial distribution where the number of successes (r) is equal to 1.

source: stattrek.com
Multistage Sampling
Multistage Sampling

Definition: The Multistage Sampling is the probability sampling technique wherein the sampling is carried out in several stages such that the sample size gets reduced at each stage. The multistage sampling is a complex form of cluster sampling.

Normal, Log-Normal, Student's t, and Chi-Squared
Normal, Log-Normal, Student's t, and Chi-Squared

... Student's t -distribution (or ... being compounded with a scaled inverse chi-squared distribution will lead to a t-distribution ... of Student's probability ...

Poisson
Poisson

In probability theory and statistics, the Poisson distribution (French pronunciation: ​; in English often rendered /ˈpwɑːsɒn/), named after French mathematician Siméon Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur ...

Simple Random Sampling (SRS)
Simple Random Sampling (SRS)

A subset of a statistical population in which each member of the subset has an equal probability of being chosen. A simple random sample is meant to be an unbiased representation of a group. An example of a simple random sample would be a group of 25 employees chosen out of a hat from a company of 250 employees.

Simple Random Sampling (SRS)
Simple Random Sampling (SRS)

A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen. An example of a simple random sample would be the names of 25 employees being chosen out of a hat from a company of 250 employees.

Stratified Sampling
Stratified Sampling

Stratified sampling is a probability sampling technique wherein the researcher divides the entire population into different subgroups or strata, then randomly selects the final subjects proportionally from the different strata.

Systematic Sampling
Systematic Sampling

Systematic sampling is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point and a fixed, periodic interval. This interval, called the sampling interval, is calculated by dividing the population size by the desired sample size.