We can rarely go and count all the individuals in an animal population. Instead we have to take a sample and infer the
population from the sample. Mark-recapture is one 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 we are uncertain about the true value of the population. How uncertain? That's the question we work toward answering this week.
Monday we see the fundamental elements of combinatorics, one principle and two formulas: the Multiplication Principle, and Permutations & Combinations. If you have taken, or are in, an introductory stats course these may already 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.
Assignment 10 is due on a Thursday, sort of...
This week's assignment would normally fall due on a Friday, but that's Good Friday, a holiday, and after decades of in-person teaching it just feels wrong to make something due on a holiday. So its official due date is the Thursday. But I won't mark it before the Monday so...
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 of the course. Don't lose your grip now! 💪
Office Hours
I'll be in my
Zoom
"office" again this week on Monday, Wednesday and Friday
from
10:30 am to 11:30 am. Come on by if you have questions.
That's all for now!
Try to harness your spring fever and use it for good,
or at least mathematics 😉,
Tim
It is likely that unlikely things should happen. —Aristotle
