It is a type of continuous probability distribution for a random variable. It is also called as Normal distribution.

The general form of its probability density function is;

Here the parameter µ is the mean or expectation of the distribution and σ is the standard deviation.

When the mean becomes 0 and variance becomes 1 in a Gaussian distribution, it becomes a Standard Normal Distribution.

Gaussian distribution follows a bell-shaped curve and hence generally known as a bell curve.

Let us consider a random variable *'X'* such that *'X'* belongs to Gaussian distribution.

**X∈G(µ,σ)**

The mean is given as

The variance is given as

The Standard deviationσ=√variance

Now we look onto the empirical formula in Gaussian distribution.

• The first empirical formula is given as

**P(µ-σ≤X≤µ+σ)≈68%**.

i.e.,68% of the total distribution will be present in the first standard deviation range.

• The second empirical formula is given as

**P(µ-2σ≤X≤µ+2σ)≈95%**.

This means that 95% of the total distribution will be present in the second standard deviation range.

• The third empirical formula is given as

**P(µ-3σ≤X≤µ+3σ)≈99.7%**.

This means that 99.7% of the total distribution will be present in the third standard deviation range.

Now we look onto what is called as log-normal distribution.

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**Log-Normal Distribution**

Consider a random variable ‘X’ such that it has the datapoints

**X={x1,x2,x3,…..,xn)}**

Then **ln(X)={ln(x1),ln(x2),ln(x3),…..,ln(xn)}**

We say that this random variable *'X'* belongs to log-normal distribution if *ln(X)* is normally distributed and follows the Gaussian distribution.

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