Types of Random Variables in Probability Distribution
There are following two types of
- Discrete Random Variables
- Continuous Random Variables
Discrete Random Variables in Probability Distribution
A Discrete Random Variable can only take a finite number of values. To further understand this, let’s see some examples of discrete random variables:
- X = {sum of the outcomes when two dice are rolled}. Here, X can only take values like {2, 3, 4, 5, 6….10, 11, 12}.
- X = {Number of Heads in 100 coin tosses}. Here, X can take only integer values from [0,100].
Continuous Random Variable in Probability Distribution
A Continuous Random Variable can take infinite values in a continuous domain. Let’s see an example of a dart game.
Suppose, we have a dart game in which we throw a dart where the dart can fall anywhere between [-1,1] on the x-axis. So if we define our random variable as the x-coordinate of the position of the dart, X can take any value from [-1,1]. There are infinitely many possible values that X can take. (X = {0.1, 0.001, 0.01, 1,2, 2.112121 …. and so on}.
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