Introduction to Data Science Probability Distributions Introduction

Probability Distribution

Probability Distribution is defined as a mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment.

Let us consider an Example of tossing a coin, the possible outcomes are head or a tail ,

The probability of getting a head is \frac{1}{2} ,similarly for getting a tail is also the same which is \frac{1}{2} .

In the case of rolling a die, the possible outcomes is getting a number from 1 to 6,

And for getting “1” after rolling a die is \frac{1}{6} , similarly for getting  “2”,”3”,”4”,”5”,”6” is also the same which is \frac{1}{6}  respectively .

 

A probability distribution function is formally defined by a Cumulative Distribution Function(CDF) ,

The CDF of a real-valued random variable X ,evaluated at x , is the probability that X will take less than or equal to x

We can write it mathematically as

 

F_x (x) = P ( X \leq x )

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