A random variable is a variable whose value is unknown or a function that assigns values to each of an experiment’s outcomes.
Random variables are often designated by letters and can be classified as discrete, which are variables that have specific values, or [[Y1Q2/Simulating and Modelling to Understand Change/Module I - Introduction & Random Variables Simulation/Random Variable Simulation/Continuous Random Variables|continuous]], which are variables that can have any values within a continuous range.
The use of random variables is most common in probability and statistics, where they are used to quantify outcomes of random occurrences.
Random variables are required to be measureable and are typically real numbers.
For example, the letter X may be designated to represent the sum of the resulting numbers after three dice are rolled.
A random variable is different from an algebraic variable
The variable in an algebraic equation is an unknown value that can be calculated. e.g. x+7=10
A random variable has a set of values, and any of those values could be the resulting outcome.
A random variable has a probability distribution that represents the likelihood that any of possible values would occur. It can be discrete or continuous.
Variable: There is some process that takes some value. It is a synonym of function as you have studied in other mathematics classes.
Random: The variable takes values according to some probability distribution.
Discrete: This refers to the possible values that the variable can take. In this case, it is a countable (possibly infinite) set of values.
In general, we denote a random variable as X and its possible values as $X={X_1, X_2, X_3,…}$. Examples:
- Number of donuts sold in a day in a shop {0,1,2,3,…}. Non-negative integers, infinite values.
- Outcome of a Covid-19 test {0,1}
- Number shown on the face of a dice {1,2,3,4,5,6}
Discrete Descriptive Statistics