# Random Variables, Expectations, and More About Games

• Richard Isaac
Part of the Undergraduate Texts in Mathematics book series (UTM)

## Abstract

Suppose we toss a coin three times in independent trials, with probability p of getting a head at each trial. On the average, how many heads can we expect to get? Right now this question does not have a precise meaning for us; what do we mean by “average” or “expect”? Most likely we do have a rough idea of the meaning of the question. Three tosses of a coin will result in anywhere from 0 to 3 heads, so the answer must be some number in that interval. The first step in making the question precise is the definition of the term random variable. A random variable is a correspondence that assigns to each outcome in a sample space a unique number. (Mathematicians more generally refer to such objects as functions.) For example, in the above setup of three tosses of a coin, let X = the total number of heads obtained The table below shows the assignment of a value for X to each of the eight possible outcomes.

## Keywords

Discrete Random Variable Bernoulli Trial Fair Coin Expected Income Casino Game
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.