RandomVariables.md (857B)
1 # Random Variables 2 3 L4 + Khan 4 5 **Definition:** Random variables in stats and probability are functions that map processes to outcomes that depend on random events. 6 7 Random variables, despite the name, are functions not variables. 8 9 A random variable is any function that depends on randomness. In this way, a mapping from a value to a real number and then multiplying it by a scalar can be composed of two random variables. The first one maps to the real number takes a random input and outputs a value x times more than the input. 10 11 ## Formal 12 13 A function from omega (sample space) to the real numbers (discrete or continuous does not matter). 14 15 ## Example 16 17 Example: 18 19 X = {1 if heads} 20 {0 if tails} 21 22 Geometric random variables are random variables that result in [ProbabilityMassFunction](ProbabilityMassFunction.md) with a geometric shape (see PMF for more).