Chapter 5: Discrete Probability Distributions
... In our Yankees-Red Sox example, the variable "number of games won by the Yankees" is a discrete random variable since it can only take on values of 0, 1, 2, or 3. Any values in between simply aren't possible. For example, winning 1.264 games or 2.835 games just couldn't happen. Total runs scored or number of pitchers used in the series would likewise be considered discrete random variables.
On the other hand, variables like the length of time it takes to complete the series or the quantity of soda consumed during the games would be classified as continuous random variables; each can take on any value within a specified range. The total time it takes to finish the series might, for example, be anywhere in the interval 9 to 18 hours. The amount of soda consumed at the games might vary anywhere in a range of, say, 0 to 5,000 gallons. What makes these variables continuous is the fact that between any two points in the relevant range, there are an infinite number of values that the random variable could take on. This same property makes variables like height, weight and age continuous...
Chapter 7: Statistical Inference
... You'll next have to settle on a procedure to determine just which students to pick. In general, we'll want a selection procedure that has a reasonable chance of producing a "representative" sample-- a sample that looks more or less like the population it's intended to represent.
Although any number of selection procedures are available, some would clearly fall short of producing an acceptable sample. For example, standing on the library steps on Friday afternoon and stopping the first 50 students coming out the door might be a convenient way to pick a sample, but it's unlikely to produce a sample that truly represents the general student population. The same might be said for choosing your entire sample from the group of students sleeping on the lawn...
Chapter 9: Hypothesis Testing
... Now that we've set Montclair's position as the null hypothesis, our plan is to randomly sample 50 axles and use sample results to decide whether or not to reject Montclair's claim. Evidence that would convince us to reject Montclair's claim will come in the form of a sample result so unlikely under an assumption that the null hypothesis is true that a reasonable person would have to conclude that the null hypothesis isn't true. The trick now is to clearly identify these sorts of "unlikely" results.....