Probability and Statistics
Stuid
Probability and statistics are key concepts in the subject of mathematics. While probability is all about chance, statistics involves handling data using different techniques.
With the help of ‘statistics’ we can represent complicated data in an easy and understandable way. It is an important component of data science professions. Professionals utilize statistics in their business predictions. It helps them in calculating future profit or loss of their respective companies.
Probability indicates the likelihood of the outcome of any random event. It ‘examines’ the extent to which any event is likely to happen.
Example:
What is the possibility of getting a head if we flip a coin in the air?
All of us know that either head or tail will be the outcome.
Hence, the probability of head = ½.
Probability is the measure of the possibility of an event to happen. It calculates the certainty of the event.
Formula:
P(E) = No: of favorable outcomes/no: of total outcomes
i.e. P(E) = n(E)/n(S)
Here,
n(E) denotes the number of events favorable to event E.
n(S) denotes the total number of outcomes.
Statistics
The study of collection, analysis, interpretation, presentation and organization of data is known as statistics. It is typically a method of collecting/summarizing data. Statistics has a wide variety of applications. It helps us in studying the population of a country, its economy etc.
Statistics aids subjects such as sociology, geology, and also helps in weather forecasting. The data collected can either be quantitative or qualitative. There are two types of quantitative data, namely discrete and continuous. While discrete data has a fixed value, continuous data is not a fixed data, it has a range. Several terms and concepts are deployed in statistics.
Terms
Random experiment, sample space, independence and variance are some of the common terms used in statistics and probability.
Random Experiment
In a random experiment, we will not be able to predict the result of the experiment until it is noticed.
For example, if we throw a dice randomly, we may get any output between 1 to 6. This is an example of a random experiment.
Sample Space
The set of all possible results/outcomes of a random experiment is known as sample space.
For example, if we throw a dice randomly, the sample space for the experiment will include all the possible outcomes of throwing a dice.
Hence, sample space = {1,2,3,4,5,6}
Random Variables
The variables which denote the possible outcomes of a random experiment are known as random variables. The two types of random variables are discrete random variables and continuous random variables.
While discrete random variables take distinct values that are countable, continuous random variables can take an infinite number of possible values.
Independent Event
Two events are termed as independent of each other if the probability of occurrence of one event has no impact on the probability of another event. For example, if a coin is flipped and a dice is thrown at the same time, the probability of getting a ‘head’ will be independent of the probability of getting a ‘6’ in dice.
Mean
The average of the random values of the possible outcomes of a random experiment is the mean of a random variable. It is also known as the expectation of a random variable.
Expected Value
The mean of a random variable is known as expected value. It is basically the assumed value that is considered for an experiment. It is also known as expectation/first moment.
Example: When we roll a dice (six faces), the average value of all the possible outcomes (( i.e. 3.5.) will be the expected value.
Variance
Variance explains how the values of the random variable are spread around the mean value. The distribution of the sample space across the mean is specified.
In this blog, we have discussed about statistics and probability.
Probability indicates the likelihood of the outcome of any random event. It ‘examines’ the extent to which any event is likely to happen.
The study of collection, analysis, interpretation, presentation and organization of data is known as statistics.
The set of all possible results/outcomes of a random experiment is known as sample space.