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# Probability and Statistics

# I Like Abstract Stuff; Why Should I Care?

Mathematicians deal with two different kinds of numbers.

**Discrete** numbers are numbers that have obvious gaps between them, like Letterman's teeth. For example, integers are discrete: there's a huge, obvious gap between the numbers 1 and 2, and there are no other integers between them.

**Continuous** numbers are numbers where no matter how close two of them are, there's another number between them. The real numbers are continuous: Even if we get two numbers as close together as 0.111 and 0.1111, we can still find a number in between them: for example, 0.11105.

Our study of probability has been dealing with discrete numbers (the number of marbles in a jar, or socks in a drawer), but mathematicians also study probabilities involving continuous numbers. If you have 0.111 socks in your drawer, it's time to go sock shopping.

If you take a data set and make histograms with thinner and thinner rectangles, you see pictures that are getting increasingly closer to something called a **probability distribution**, which is usually studied in calculus and beyond. Now that we've planted that irresistible little seed of anticipation in your noggin, let's wrap this puppy up.