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Statistics : Probability Distribution Tutorials

Poisson Distribution Example

  • STATISTICS
Poisson distribution In this tutorial, we will provide you step by step solution to some numerical examples on Poisson distribution to make sure you understand the Poisson distribution clearly and correctly. Definition of Poisson Distribution A discrete random variable $X$ is said to have Poisson distribution with parameter $\lambda$ if its probability mass function is $$ \begin{equation*} P(X=x)= \left\{ \begin{array}{ll} \frac{e^{-\lambda}\lambda^x}{x!} , & \hbox{$x=0,1,2,\cdots; \lambda>0$;} \\ 0, & \hbox{Otherwise.} \end{array} \right.
3 min Read 2

Hypergeometric Distribution Examples

  • STATISTICS
Hypergeometric Experiment In this tutorial, we will provide you step by step solution to some numerical examples on hypergeometric distribution to make sure you understand the hypergeometric distribution clearly and correctly. Definition of Hypergeometric Distribution Suppose we have an hypergeometric experiment. That is, suppose there are $N$ units in the population and $M$ out of $N$ are defective, so $N-M$ units are non-defective. Let $X$ denote the number of defective in a completely random sample of size $n$ drawn from a population consisting of total $N$ units.
4 min Read 3

Normal Distribution Examples

  • STATISTICS
Normal Distribution A continuous random variable $X$ is said to have a normal distribution if its probability density function is given by $$ \begin{equation*} f(x;\mu, \sigma^2) = \left\{ \begin{array}{ll} \frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{1}{2\sigma^2}(x-\mu)^2}, & \hbox{$-\infty< x<\infty$, $-\infty<\mu<\infty$, $\sigma^2>0$;} \\ 0, & \hbox{Otherwise.} \end{array} \right. \end{equation*} $$ where $\mu$ and $\sigma^2$ are the parameters of normal distribution. In notation it can be written as $X\sim N(\mu,\sigma^2)$. Mean Normal distribution The mean of $N(\mu,\sigma^2)$ distribution is $E(X)=\mu$.
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Weibull Distribution Examples - Step by Step Guide

  • STATISTICS
Weibull Distribution In this tutorial we will discuss about the Weibull distribution and examples. Weibull distribution is a continuous probability distribution. Weibull distribution is one of the most widely used probability distribution in reliability engineering. This tutorial help you to understand how to calculate probabilities related to Weibull distribution and step by step guide on Weibuill Distribution Examples for different numerical problems. Three parameter Weibull Distribution A continuous random variable $X$ is said to have a Weibull distribution with three parameters $\mu$, $\alpha$ and $\beta$ if the probability density function of Weibull random variable $X$ is
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