We can't usually go and count all the individuals in an animal population. Instead we have to take a sample and infer the
population from our sample. Mark-recapture is a common way of doing this. We capture a sample of the population, mark them and release them back into the environment. Sometime later we capture a second sample that will contain some marked and some unmarked animals. We can infer the total population from the ratio of marked (recaptured) to unmarked animals in the second sample. But the result is an estimate, and so we are uncertain about the true value of the population. How uncertain? That's the question we work towards answering this week.
Monday we see the fundamental elements of combinatorics, one principle and two formulas: the Multiplication Principle, and formulas for Permutations & Combinations. If you have taken, or are in, an introductory stats course these may be familiar to you.
Wednesday we play with a Quincunx, and then flip some coins, and then discover that mathematicians have ruined it all by naming these things Bernoulli trials and Binomial distributions. 😆
Friday we will put our tools to use to determine the likelihood of our estimate of the number of fish in the lake.
Bring-your-calculator-to-class week
We will be using our calculators a lot this week, focussing on some buttons that may be new to you, so don't forget to bring yours with you.
The last fresh start + Don't lose your grip now!
This week will complete our brief look at modelling uncertainty using probability. Next week we begin the final three-week section of the course on Graph Theory. It gives you your last fresh start of the course, and marks the beginning of the home stretch. Don't lose your grip now! 💪
Will this work?
The next two items were in last week's email, but surveys from previous years suggest there's only a 50% chance that you read the entire email last week. By repeating them here do I guarantee that everyone will have read it, since 50% + 50% = 100%?
Advice: Before you begin an assignment or exercise
Pro tip
for doing exercise and assignment problems: Begin by preparing a one-page summary of the
week's material and keep it at your side.
Preparing the page is
an excellent way of warming up to do the problems, and then you'll have all the formulas and diagrams you need
handy. Even better, when the time comes to
create your cheat sheet for the final exam you can just make it up from your 13 weekly
formula pages. Some weeks I have provided a formula sheet that you can use as a starting
point (by printing it out and annotating it), but when I haven't, I strongly encourage you to create
one of your own. Cheatsheets rule! 😎
Collaborate! Do research! Just don't copy.
A reminder about how I feel about students working together, and about students doing research (google) to find
answers: I love both these things!
Working with other people can help you catch small errors you could get stuck on, suggest
approaches that would not have occurred to you, and keep your spirits up. If you're stuck on
a problem, e.g. a proof, turning to the web is a natural thing to do. The goal is for you to
learn and come to an understanding of the course material. If other people or other resources
can help you do that then I'm all for them. Of course you shouldn't just copy someone else's
work, because that wouldn't help you form an understanding. And you should acknowledge your
sources when you've looked things up. But you already know that. 😏
