The Data Science Journey

This article tries to look at the Normal Distribution in somewhat of a different angle. Most of us have seen the probability density function and the famous bell shaped curve very often . So through this article I want you to gain a different insight about the same. If you have a background in mathematics or statistics , you must be familiar with the following bell shaped curve and the somewhat difficult looking and inherently less intuitive function :P If not , let me introduce them as the Normal distribution and its Probability Density Function.                    Let's try and get familiarized with both of these :) We consider a simpler case , where μ = 0 and σ = 1, that is the case of Standard Normal Distribution. However , all the things apply to normal distribution also. So , we have : Let's try and break down the the function (probability density fu...

Law of Large Numbers  In this article we attempt to understand the concept of Law of Large numbers in Statistics . The idea is basically to see both the sides of statistics , the experimental side using computation and also the theoretical aspect using mathematics. An Experiment : So we take the experiment of rolling a dice (Let this Event be X). Theoretically the Expected Value (Mean) of this event is calculated as follows : Assuming it's a fair dice , so each of the possible outcomes in the Sample Space = {1,2,3,4,5,6} have an equal probability of occurrence and hence probability of getting say a value ' i ' where i belongs to the sample space P(K = i) = 1/6 So, we can compute Expectation of this event as E[X] = (1+2+3+4+5+6)/6 = 3.5. This is the theoretical definition of what an expectation for this event would look like. Now , comes the experimental part of this exercise , So supposedly we roll a single dice and note down the outcome. Say we got the outcome Xi = xi f...