If X and Y are independent Gaussian random variables with mean 0 and standard deviation sigma, then sqrt(X^2 + Y^2) has a Rayleigh distribution with parameter sigma.
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Actually the normal distribution is the sub form of Gaussian distribution.Gaussian distribution have 2 parameters, mean and variance.When there is zero mean and unit variance the Gaussian distribution becomes normal other wise it is pronounced as Gaussian.Wrong! The standard normal distribution has mean 0 and variance 1, but a normal distribution is the same as the Gaussiand, and can have any mean and variance. Google stackexcange "what-is-the-difference-between-a-normal-and-a-gaussian-distribution"
First i will explain the binomial expansion
A probability density function (pdf) for a continuous random variable (RV), is a function that describes the probability that the RV random variable will fall within a range of values. The probability of the RV falling between two values is the integral of the relevant PDF. The normal or Gaussian distribution is one of the most common distributions in probability theory. Whatever the underlying distribution of a RV, the average of a set of independent observations for that RV will by approximately Gaussian.
If the process can be assumed to follow a Gaussian distribution then 99.7% of the outputs of the process will lie between those two limits. That may be of benefit in quality control if it is a production process.
A simple continuous distribution can take any value between two other values whereas a discrete distribution cannot.