Introduction
A mathematical function that provides the probabilities of occurrence of various possible outcomes in an experiment is Probability Distribution. It is the possibility/ probability of every possible outcome of an experiment. Let’s understand Probability Distribution with an example, let x be a random variable and denote the outcome of a roll of a dice, then the probability distribution of x can be denoted as-
It can be observed that the sum of all P(X) = 1.
Types of Probability Distribution
Probability distribution is of two types: Discrete and Continuous Probability Distribution.
- If the probabilities of the random variable take only a discrete set of values, then the distribution is called a discrete probability distribution. For example, the probability distribution of a random variable denoting the outcome of a roll of dice.
- If the probabilities of the random variable take any value between two numbers i.e. a range of values then the distribution is called a continuous probability distribution. For example, the probability distribution of a random variable denoting the temperature throughout the day.
Cumulative Distribution Function
It is the probability that a random variable X will take a value less than or equal to x. For a discrete random variable,
F(x) = P(X<=x) = P(a)
For a continuous random variable,
F(x) = P(X<=x) = f(x)dx
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