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Probability Distribution Calculators

Log Normal Distribution Calculator

  • STATISTICS
Definition of 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 \[ \begin{equation*} f(x;\mu,\sigma) =\left\{ \begin{array}{ll} \frac{1}{\sqrt{2\pi}\sigma x}e^{-\frac{1}{2\sigma^2}(\ln x -\mu)^2}, & \hbox{$x\geq 0$;} \\ 0, & \hbox{$x < 0$.} \end{array} \right. \end{equation*} \] $\mu$ is location parameter $\sigma$ is scale parameter Log-Normal Probability Calculator First Parameter ($\mu$) Second parameter ($\sigma$) P(X< A) P(X > B) P(A< X < B) and Outside A and B and Calculate Results Mean : Variance : Required Probability :

Negative Binomial Distribution Calculator

  • STATISTICS
Negative Binomial Distribution Calculator Use Negative Binomial Distribution Calculator to find the probability and cumulative probabilities for negative binomial random variable given the number of successes ($r$) and probability of success ($p$). Calculator Negative Binomial Distribution Calculator Number of successes (r): Number of failures (x): Probability of success (p): Calculate Negative Probability Calculator Result Probability : P(X = x) Cumulative Probability : P(X ≤ x) Cumulative Probability : P(X < x) Cumulative Probability : P(X ≥ x) Cumulative Probability : P(X > x) How to use Negative Binomial Distribution Calculator?

Normal Approximation to Binomial Distribution2 Calculator

  • STATISTICS
Normal Approximation to Binomial Distribution Let $X$ be a binomially distributed 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 $n$ is sufficiently large if $np \geq 5$ and $n(1-p)\geq 5$. For sufficiently large $n$, $X\sim N(\mu, \sigma^2)$.

Normal Approximation to Poisson Distribution Calculator

  • STATISTICS
Normal Approximation to Poisson Distribution Calculator Normal distribution can be used to approximate the Poisson distribution when the mean of Poisson random variable is sufficiently large.When we are using the normal approximation to Poisson distribution we need to make correction while calculating various probabilities. Let $X$ be a Poisson distributed random variable with mean $\lambda$. The mean of $X$ is $\mu=E(X) = \lambda$ and variance of $X$ is $\sigma^2=V(X)=\lambda$. The general rule of thumb to use normal approximation to Poisson distribution is that $\lambda$ is sufficiently large (i.

Normal Distribution Calculator

  • STATISTICS
Definition of Normal Distribution A continuous random variable $X$ is said to have an normal distribution with parameter $\mu$ and $\sigma$ if its p.d.f. is given by $$ \begin{equation*} f(x)=\left\{ \begin{array}{ll} \frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{1}{2}\big(\frac{x-\mu}{\sigma}\big)^2}, & \hbox{$-\infty< x<\infty ;-\infty < \mu < \infty; \sigma^2>0$;} \\ 0, & \hbox{Otherwise.} \end{array} \right. \end{equation*} $$ Normal Probability Calculator Mean ($\mu$) Standard deviation ($\sigma$) P(X< A) P(X > B) P(A< X < B) and Outside A and B and Calculate Results Required Probability :

Poisson Approximation to Binomial Distribution Calculator

  • STATISTICS
Poisson Approximation to Binomial Distribution Calculator Let $X$ be a binomially distributed random variable with number of trials $n$ and probability of success $p$. The general rule of thumb to use Poisson approximation to binomial distribution is that the sample size $n$ is sufficiently large and $p$ is sufficiently small such that $\lambda=np$ (finite). For sufficiently large $n$ and small $p$, $X\sim P(\lambda)$. Use Poisson Approximation to Binomial Distribution Calculator to find the mean,standard deviation and required probability based on number of trials,probability of success and values.

Poisson Distribution Calculator

  • STATISTICS
Poisson Distribution Calculator Poisson distribution calculator is used to find 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 < x) Cumulative Probability : P(X ≥ x) Cumulative Probability : P(X > x) Poisson Distribution A discrete random variable $X$ is said to have Poisson distribution with parameter $\lambda$ if its probability mass function is

Weibull Distribution Calculator

  • STATISTICS
Weibull Distribution Calculator Use this calculator to find the probability density and cumulative probabilities for two parameter Weibull distribution with parameter $\alpha$ and $\beta$. Weibull Distribution Calculator Location parameter $\alpha$: Scale parameter $\beta$ Value of x Calculate Results Probability density : f(x) Probability X less than x: P(X < x) Probability X greater than x: P(X > x) Definition of Weibull Distribution The pdf of two parameter Weibull distribution with parameters $\alpha$ and $\beta$ is given by

Binomial Distribution Calculator with Steps by Steps Solution

  • STATISTICS
Binomial Distribution Calculator Binomial distribution calculator is used to find the probability and cumulative probabilities for binomial random variable given the number of trials ($n$) and probability of success ($p$). It also calculate mean of binomial distribution,variance of binomial distribution. Binomial Probability Calculator Binomial Probability Calculator Number of trials ($n$): Number of success (x): Probability of success ($p$): Binomial Calculate Binomial Distribution Calculator Result Mean : $np$ Variance : $np(1-p)$ Probability : P(X = x) Cumulative Probability : P(X ≤ x) Cumulative Probability : P(X < x) Cumulative Probability : P(X ≥ x) Cumulative Probability : P(X > x) How to use Binomial Distribution Calculator with step by step?

Normal Approximation to Binomial Distribution Calculator with Examples

  • STATISTICS
Normal Approximation to Binomial Distribution Calculator Normal approximation allows you to estimate binomial probabilities using the normal distribution. While the binomial distribution is vital tool in statistics used to calculate the probability of success in the a series of independent trials. However, calculating the exact probabilities for the binomial distribution can become tedious, expecially with numerous trials. The built-in calculator allows you to easily estimate the binomial probabilities using the normal distributions.

Uniform Distribution Calculator

  • STATISTICS
Uniform Distribution Calculator computes probability density and cumulative probabilities associated with continuous uniform distribution. This distribution is characterized by a constant probability density function over a specified interval. 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. Use this Uniform distribution calculator to calculate probability density,probability X less than x and probability X greater than x using minimum value of alpha, maximum value of beta,value of x.