What is Probability Distribution?

Probability Distribution is defined as the function that gives the probability of all the possible values of the random variables. There are various types of probability distribution, which are Binomial Distribution, Bernoulli Distribution, Normal Distribution, and Geometric Distribution.

Probability Distribution Definition

Probability Distribution is the set of all possible outcomes of any random experiment or event. It tells how the probability of an event is distributed for different values of random variables.

Probability Distribution Function

Probability Distribution Function is a function in mathematics that gives the probability of all the possible outcomes of any event. We define probability distribution as how all the possible probabilities of any event are allocated over the distinct values for an unexpected variable.

Two functions are used to describe the Probability Distribution of the function which includes, Probability Mass Function and Probability Distribution Function. Here in this article, we will learn about the Probability Distribution Function. There are two ways to represent the data, Discrete Data and Continuous Data, and based on that we can represent the Probability Distribution Function into two further categories.

In this article, we will learn about Probability Distribution, Probability Distribution Function, its Formula, Graphs, related Examples, and others in detail.

Table of Content

  • What is Probability Distribution?
    • Probability Distribution Definition
  • Probability Distribution Function
    • Probability Distribution Function Definition
  • Probability Distribution Function Formula
    • Probability Distribution of a Discrete Random Variable
    • Probability Distribution of a Continuous Random Variable
    • Normal Probability Distribution Formula
    • Binomial Probability Distribution Formula
  • Probability Distribution Graph
  • Probability Distribution Function and Probability Density Function
  • Uses of Probability Distribution Function
  • Probability Distribution Function Examples
  • Practice Questions on Probability Distribution Function

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What is Probability Distribution?

Probability Distribution is defined as the function that gives the probability of all the possible values of the random variables. There are various types of probability distribution, which are Binomial Distribution, Bernoulli Distribution, Normal Distribution, and Geometric Distribution....

Probability Distribution Function

Probability Distribution Function is defined as the function that is used to express the distribution of a probability. It is also called Cumulative Distribution Function(CDF). For any random variable X where its value is evaluated at the points ‘x’, then the probability distribution function gives the probability that X takes the value less than equal to x. We represent the probability distribution as, F(x) = P (X ≤ x)...

Probability Distribution Function Formula

Probability distribution function formula gives the probability of the all the possible outcomes of any random variable. On the basis of types of random variable the different formula for the probability distribution function are,...

Probability Distribution Graph

The graph that plot the Probability Distribution Functions are called the Probability Distribution graphs. These graphs helps us to visualise the probability distribution around a random variable and help us to easily find the required solution....

Probability Distribution Function and Probability Density Function

We easily describe the Probability Ditribution using Probability Distribution Function and Probability Density Function. Using a probability distribution function is very useful for both continuous probability distribution and discrete probability distribution, while probability density function(pdf) is only used for continuous probability distribution....

Uses of Probability Distribution Function

Statistical Inference: PDFs are fundamental in statistical inference, allowing for the estimation of population parameters and hypothesis testing. Modeling and Simulations: PDFs are used to model real-world phenomena and to simulate random processes in fields like engineering, finance, and the natural sciences. Risk Assessment: In finance and insurance, PDFs help assess risks and determine the likelihood of various financial outcomes....

Probability Distribution Function Examples

Example 1: Suppose we toss two dice. Make a table of the probabilities for the sum of the dice. The possibilities are: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12....

Practice Questions on Probability Distribution Function

Q1: Find the Probability Distribution of Number of Heads when two coins are tossed Simultaneously....

FAQs on Probability Distribution Function

What is Probability Distribution Function?...