The random variable is a discrete random variable when its range is finite (or countably infinite). One way is to use an arrow diagram to represent the mappings between each element. 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 \(x\)). The random variable is a continuous random variable when its range is uncountably infinite. Specifically, the notation X = x signifies the event that the random variable X assumes the particular value x. Discrete Mathematics - Functions - A Function assigns to each element of a set, exactly one element of a related set. Probabilities of Discrete Random Variables. 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. Describing a function graphically usually means drawing the graph of the function: plotting the points on the plane. Functions can be written as above, but we can also write them in two other ways. In discrete math, we can still use any of these to describe functions, but we can also be more specific since we are primarily concerned with functions that have \(\N\) or a finite subset of \(\N\) as their domain. ; Continuous random variables. {list each element in the set} examples: W h oa re ts ud nig y w? 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. The O-notation describes upper bounds on how fast functions grow. Often one looks for a simple function g that is as small as possible such that still f is O(g). What are the shoe sizes of the students in your row? Where is typically or in discrete probability and in continuous probability.. 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