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 $$ \begin{equation*} f(x;\mu, \sigma^2) = \left\{ …
In this tutorial we will discuss some numerical examples on Poisson distribution where normal approximation is applicable. For large value of the $\lambda$ (mean of Poisson variate), the Poisson distribution can be well approximated by a normal distribution with the same mean and variance. Normal approximation to Poisson distribution Examples Let $X$ be a Poisson …
Normal Approximation to Binomial Calculator with examples Let $X$ be a Binomial random variable with number of trials $n$ and probability of success $p$. The mean of $X$ is $\mu=E(X) = np$ and variance of $X$ is $\sigma^2=V(X)=np(1-p)$. The general rule of thumb to use normal approximation to binomial distribution is that the sample size …
Log-normal Distribution The continuous random variable $X$ has a log-normal distribution if the random variable $Y=\ln (X)$ has a normal distribution with mean $\mu$ and standard deviation $\sigma$. The probability density function of $X$ is $$ \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, …
