Continuous Uniform Distribution Calculator With Examples The continuous uniform distribution is the simplest probability distribution where all the values belonging to its support have the same probability density. It is also known as rectangular distribution. This tutorial will help you understand how to solve the numerical examples based on continuous uniform distribution. Continuous Uniform Distribution …
Poisson Distribution Calculator Poisson distribution calculator helps you to determine the probability and cumulative probabilities for Poisson random variable given the mean number of successes ($\lambda$). Poisson Distribution Calculator Average rate of success ($\lambda$): Number of success (x): Calculate Result Probability : P(X = x) Cumulative Probability : P(X ≤ x) Cumulative Probability : P(X …
Chebyshev’s Inequality Chebyshev’s Inequality is a very powerful inequality, because it applies to any probability distribution. Chebyshev’s Inequality is used to estimate the probability that a random variable $X$ is within $k$ standard deviation of the mean. Before we derive Chebyshev’s Inequality, let us derive the Chebyshev’s Theorem. Chebyshev’s Theorem If $g(x)$ is a non-negative …
Normal Distribution Normal distribution is one of the most fundamental distribution in Statistics. It is also known as Gaussian distribution. Definition of Normal Distribution A continuous random variable $X$ is said to have a normal distribution with parameters $\mu$ and $\sigma^2$ if its probability density function is given by $$ \begin{equation*} f(x;\mu, \sigma^2) = \left\{ …
In this tutorial we will discuss some numerical examples on Poisson distribution where normal approximation is applicable. For large value of the $\lambda$ (mean of Poisson variate), the Poisson distribution can be well approximated by a normal distribution with the same mean and variance. Normal approximation to Poisson distribution Examples Let $X$ be a Poisson …
Hypergeometric Distribution A hypergeometric experiment is an experiment which satisfies each of the following conditions: The population or set to be sampled consists of $N$ individuals, objects, or elements (a finite population). Each object can be characterized as a "defective" or "non-defective", and there are $M$ defectives in the population. A sample of $n$ individuals …
Normal Approximation to Binomial Calculator with examples Let $X$ be a Binomial random variable with number of trials $n$ and probability of success $p$. The mean of $X$ is $\mu=E(X) = np$ and variance of $X$ is $\sigma^2=V(X)=np(1-p)$. The general rule of thumb to use normal approximation to binomial distribution is that the sample size …
Poisson approximation to binomial distribution examples Let $X$ be a binomial random variable with number of trials $n$ and probability of success $p$. The mean of $X$ is $\mu=E(X) = np$ and variance of $X$ is $\sigma^2=V(X)=np(1-p)$. The general rule of thumb to use Poisson approximation to binomial distribution is that the sample size $n$ …
Log-normal Distribution The continuous random variable $X$ has a log-normal distribution if the random variable $Y=\ln (X)$ has a normal distribution with mean $\mu$ and standard deviation $\sigma$. The probability density function of $X$ is $$ \begin{aligned} f(x) & = \frac{1}{\sqrt{2\pi}\sigma x}e^{-\frac{1}{2\sigma^2}(\ln x -\mu)^2},x\geq 0 \end{aligned} $$ In Log-normal distribution $\mu$ is called location parameter, …
Cauchy Distribution Calculator Use this calculator to find the probability density and cumulative probabilities for Cauchy distribution with parameter $a$ and $b$. Cauchy Distribution Calculator Location parameter $\mu$: Scale parameter $\lambda$ Value of x Calculate Results Probability density : f(x) Probability X less than x: P(X < x) Probability X greater than x: P(X > …
