The Pleasures of Probability pp 61-76 | Cite as

# Random Variables, Expectations, and More About Games

## 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## Preview

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