Sampling from distributions

Observing the outcome of trials that involve a random variable, a variable whose value changes due to chance, can be thought of as sampling from a probability distribution—one that describes the likelihood of each member of the sample space occurring.

That sentence probably sounds much scarier than it needs to be. Take a die roll for example:

Figure 4.1: Probability distribution of outcomes of a die roll

Each roll of a die is like sampling from a discrete probability distribution for which each outcome in the sample space has a probability of 0.167 or 1/6. This is an example of a uniform distribution, because all the outcomes are uniformly as likely to occur. Further, there are a finite number of outcomes, so this is a discrete uniform distribution (there also exist continuous uniform distributions).

Flipping a coin is like sampling from a uniform...