Normal Distribution

Normal Distribution

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\{ …

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Normal approximation to Poisson distribution Examples

Normal Approx to Poisson

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 …

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Normal Approximation to Binomial Calculator with Examples

Normal Approx to Binomial

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 …

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Log Normal Distribution

Log-Normal Distribution

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, …

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