6.2 More formally

In the last section, there were initially four different possible outcomes: the four kinds of cookies that could pop out of our machine. In this situation, our sample space is the collection sample space

We also say that these four are the values of a random variable. Random variables usually have names such as X and Y. probability$random variable

A probability distribution assigns a probability to each possible outcome, which are the values of the random variable. The probability distribution for the balanced case is probability$distribution

When the probabilities are all equal, as in this case, we have a uniform distribution. probability$uniform distribution

If our sample space is finite or, at most, countably infinite, we say it is discrete. A set is countably infinite if it can be put in one-to-one correspondence with Z. sample space$discrete

The sample space is continuous if it can be put in correspondence...