Gaussian Distribution

Random variables 

• Discrete Random Variables                            

In Discrete Random Varaibles we have Whole number of data Like , Roll no , no of students. Those numbers which can't be float are Discrete Random Variables 

•  Continuous Random variables 

In continuous Random variables we have continuous value which define some Range 0-10 ,3-8 etc.

so It can be any value from the particular range ex . from Range 0-10 ,it can be 5.4,6.7 etc.

Gaussian Distribution / Normal Distribution 

Gaussian or Normal Distribution is very common term in statistics. These are generally used to represent random variables which coming into Machine Learning we can say which is something like the error when we dont know the weight vector for our Linear Regression Model. In a Gaussian distribution the more data near to the mean and is like a bell curve in general

We have two main paramters to explain or inform regarding our Gaussian distribution model they are mean and variance. Mean is usually represented by μ and variance with σ² (σ is the standard deviation). The graph is symmetrix about mean for a gaussian distribution. The mean, median and mode are equal.

So coming into μ and σ, μ is the mean value of our data and σ is the spread of our data. We can express the probability density for gaussian distribution as

While usually modelling a large data it is common that more data is closer to the mean value and the very few or less frequent data is observed towards the extremes, which is nothing but a gaussian distribution that looks like this(μ = 0 and σ = 1):

Empirical Formula of Gaussian Distribution :

              Pr(µ-sigma <= x <= µ+sigma)   ==== 68%  

             Pr(µ-2sigma <= x <= µ+2sigma) ==== 95%      (% implies that how much data is their)

             Pr(µ-3sigma <= x <= µ+3sigma) ====99%