Probability Distribution Functions: PDF, CDF, PMF

 Introduction

Statistics heavily rely on probability distribution, and in this article we will learn about the probability mass function, probability density function, and cumulative distribution function in plain English. The many functions that are used to model probability distributions are referred to by a number of terminologies in the fields of probability and statistics. They consist of:

1. Function of probability density (PDF): The PDF function calculates the likelihood that a continuous random variable will have a certain value. The likelihood that a random variable will fall inside a specific range of values is expressed mathematically. In statistics, the probability distribution of a continuous random variable is referred to as a PDF. Most frequently, PDF adheres to the Gaussian Distribution. If the features or random variables have a Gaussian distribution, then the PDF will as well. The probability of a single result on a PDF graph is always 0 since a single point reflects a line that doesn't fill the curve's area under the curve.
2. Cumulative distribution function (CDF): The likelihood that a random variable (continuous or discrete) will have a value less than or equal to a specific value is expressed by the cumulative distribution function (CDF), which is a function. It is a mathematical function that expresses the likelihood that a random variable will have a value that falls between a certain range of values and that value. Although PMF may be used to explain distributions, continuous random variables cannot be included in this description. Whether a random variable's distribution is continuous or discrete, the cumulative distribution function may be used to describe it. For instance, if a person is chosen at random and their height is X, the likelihood that they would be lower than X is F(x). If F(180 cm)=0.8, a person chosen at random has an 80% probability of being shorter than 180 cm (or, conversely, a 20% chance of being taller than 180 cm).
3. Probability mass function (PMF): The likelihood that a discrete random variable will take on a certain value is expressed by a function called the probability mass function (PMF). It is a mathematical function that expresses the likelihood that a random variable will take on a certain value as opposed to fluctuating between two or more values. The probability distribution of the discrete random variable is described by the statistical term PMF. People frequently mix up PDF with PMF. Although PMF is appropriate for discrete random variables, PDF is appropriate for continuous random variables. Throwing a dice, for instance (you can only choose between 1 and 6 numbers (countable)

About Random Variable

A random variable is one whose value is dependent on the results of the experiment and whose value is unknown to the function.

For instance, the outcome of a dice roll affects the variable value.

Regression analysis is used to find statistical relationships between variables using mostly random variables. Two categories of random variables exist, and they are:

1. Continuous random variable - Continuous random variables are those that have values that fall inside a range or interval and have an endless number of potential values. OR The term "continuous random variable" refers to variables whose values are derived by measurement. For e.g, 100 individuals on average tall, measuring rainfall
2. Discrete Random Variable - A variable with a countable number of different values is referred to as a discrete random variable. OR Discrete Random Variables are variables whose values are determined by counting. Number of students in the class, for instance.

Conclusion

In conclusion, CDFs are used to describe the likelihood that a random variable (continuous or discrete) will have a value less than or equal to a certain value, and PMFs are used to describe the likelihood that a discrete random variable will have a given value. PDFs are used to describe the likelihood that a continuous random variable will have a given value. But if you wish to learn more about them, Skillslash is one place that can be opted. At Skillslash, the project-based learning programmes and courses are excellent. The most crucial elements for students and enthusiasts who wish to succeed in this profession are packed into courses like Business analytics and Advance Data Science & AI.

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