Team:UCL/Math/Probability

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Probability

Random Variables and Probability Distributions

Random Variables

If a sample space has all of its points assigned a number, the function that is defined on this space is called a random variable, or random function. This is also known as a stochastic function/variable and is usually denoted by a capital letter such as $X$ or $Y$. For example, think of it as the probability of a random event.

If a random variable represents a finite, or countably infinite values it is known as $discrete$. An example is a list of integers. A $nondiscrete$ variable is one that represents an infinite number of possible values. An example for this could be any value between 0 and 1.

Discrete Random Distributions

A probability function is represented as follows

$$P(X=x)=f(x)$$