Probability Distribution Function
Probability Distribution Function is defined as the function that is used to express the distribution of a probability. Different types of probability, they are expressed differently. These functions are also used for Probability Density Functions for different variables.
For Normal Distribution, the Probability Distribution Function for Random Variable X is given by Fx(x) = P(X ≤ x) where X is the Random variable and P is the Probability.
The Cumulative Probability Distribution for closed interval a⇢b is given as P(a < X ≤ b) = Fx(b) – Fx(a).
In terms of integrals, the cumulative probability function is given as [Tex]F_{x}(x) = \int_{-\infty }^{x}f_{x}(t)dt [/Tex]
For Random Variable X = p, the Cumulative Probability function is given as [Tex]P(X = p) = F_{x}(p) – \lim_{x\rightarrow p}f_{x}(t) [/Tex]
Binomial Probability Distribution gives some exact values. It is often called as Probability Mass Function. For a Random Variable X and Space S where X: S⇢A where A belongs to Random Discrete Variable R, X can be defined as fx(x) = Pr(X = x) = P({s ∈ S: X(s) = x}).
Probability Distribution – Function, Formula, Table
A probability distribution is an idealized frequency distribution. In statistics, a frequency distribution represents the number of occurrences of different outcomes in a dataset. It shows how often each different value appears within a dataset.
Probability distribution represents an abstract representation of the frequency distribution. While a frequency distribution pertains to a particular sample or dataset, detailing how often each potential value of a variable appears within it, the occurrence of each value in the sample is dictated by its probability.
A probability distribution, not only shows the frequencies of different outcomes but also assigns probabilities to each outcome. These probabilities indicate the likelihood of each outcome occurring.
In this article, we will learn what is probability distribution, types of probability distribution, probability distribution function, and formulas.
Table of Content
- What is Probability Distribution?
- Probability Distribution Definition
- Random Variables
- Random Variable Definition
- Types of Random Variables in Probability Distribution
- Probability Distribution of a Random Variable
- Probability Distribution Formulas
- Expectation (Mean) and Variance of a Random Variable
- Expectation
- Variance
- Different Types of Probability Distributions
- Discrete Probability Distributions
- Bernoulli Trials and Binomial Distributions
- Binomial Distribution
- Cumulative Probability Distribution
- Probability Distribution Function
- Probability Distribution Table
- Prior Probability
- Posterior Probability
- Solved Questions on Probability Distribution