; Continuous random variables. Functions can be written as above, but we can also write them in two other ways. When discussing functions, we have notation for talking about an element of the domain (say \(x\)) and its corresponding element in the codomain (we write \(f(x)\text{,}\) which is the image of \(x\)). Discrete Mathematics - Functions - A Function assigns to each element of a set, exactly one element of a related set. E.g., f(x) = x2 + 3x is O(x2) but also O(x3), etc. Function or Not? (The word ‘simple’ is important, since trivially f is O(f).) ; Notation. Function notation Domain & Range Increasing & Decreasing Rate of Change Set Notation •notation used to represent a group of values (elements) •used with discrete &/or continuous functions 1. One way is to use an arrow diagram to represent the mappings between each element. {list each element in the set} examples: W h oa re ts ud nig y w? So the expression X = 4 would express the event that a random roll of the die would result in observing the value 4 on the upper face of the die. The random variable is a continuous random variable when its range is uncountably infinite. Often one looks for a simple function g that is as small as possible such that still f is O(g). The random variable is a discrete random variable when its range is finite (or countably infinite). Other function notation . Where is typically or in discrete probability and in continuous probability.. Discrete random variables. For the six-sided die example, x can be any integer from 1 to 6. What are the shoe sizes of the students in your row? It would also be nice to start with some element of the codomain (say \(y\)) and talk about which element or elements (if any) from the domain it is the image of. 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