Essential Maths Concepts for ML – Part 1

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Let's discuss some terms and their definitions related to statistics and probability. It will help us in brushing our concepts of probability which are essential for machine learning algorithms

Definition of Probability 

Probability is a numerical measurement which indicates the chances of occurrence of an event, say A. It is denoted by P(A). It is the ratio of favorable outcomes of an event A say m to the total outcomes of the experiment say n.

P(A) = m/n
where m represents the number of favorable outcomes of an event A and n is the total number of outcomes of the experiment.

Let's understand the experiment term in more details now.

An operation that results in a definite outcome is called an experiment
E.g. 
  1. Tossing a coin is an experiment as it can have two outcomes either Head or Tail and it is definite in number.
  2. Throwing a fair dice is an experiment as it can have only 6 outcomes which is definite in number.
Random Experiment

When the outcome of an experiment cannot be predicted with certainty, then it is called random experiment. In other words Random experiment is an experiment which may not result in the same outcome when repeated under same conditions. 

E.g.
  1. Tossing a coin is a random experiment as when coin is tossed the result may be either head or tail.
  2. Drawing a card randomly from pack of playing cards is a random experiment as it can be any one of the 52 cards.

Sample Space

The set of all possible outcomes of a random experiment is the sample space. It is generally denoted by S. 

E.g.
  1. In tossing of a coin, the outcomes are head and tail. So sample space of this experiment S = {H, T}
  2. In tossing of two coins, the sample space S will be S = {HH, TT, HT, TH}
  3. For throwing a dice, the sample space S will be S = {1, 2, 3, 4, 5, 6}

Event

Event is subset of the sample space. An event which does not contain any outcome is called as NULL event (or impossible event) and it is denoted by ϕ. 

E.g. 
  1. When throwing a dice, A= {2, 4, 6} is an event that results in the even numbers.
  2. While tossing two coins, A = {HH} is an event that results into two heads.
The outcome which belongs to an event are said to be favorable to that event. E.g. while throwing a dice, the event A = {2, 4, 6} has 3 favorable outcomes 2, 4, 6 where throw results in 2, 4, or 6.

Equally Likely Events

Two or more events are said to be equally likely if they have equal chance of occurrence.

E.g.
  1. Tossing a fair coin, the outcomes head and tail are equally likely.
  2. Throwing a fair dice, the events A = {1,3,5} and B={2,4,6} and C = {1,2,3} are equally likely.
Mutually Exclusive Events

Two or more events are said to be mutually exclusive if only one of them can occur at a time. i.e. occurrence of any of these events totally excludes the occurrence of other events.

E.g.
  1.  Tossing a coin, the outcomes head and tail are mutually exclusive.
  2. Throwing a fair dice, the events A ={ 2,4,6}  B={1,3} or C={1} are mutually exclusive events.
In my next blog we will continue discussing the mathematical concepts required to understanding the machine learning models. 

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Stay safe and healthy.

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