M347

You will enjoy M347 if…

you’re interested in why stats works mathematically
you love the idea of taking a deep dive into Bayes
you’re curious about when your data science models are valid (and when they aren’t!)
you aren’t afraid of a little algebra 😁

Four coursebooks, four extra exercise books and a handbook! (click to enlarge)

M347 units were written to be browser-friendly (bonus to hard-copy and pdf versions)…

Screencasts (short lectures) pre-recorded for many key topics.

The standard bivariate normal distribution:

\[f(z,w) = \frac{1}{2\pi \sqrt{1-\rho^2}}\exp \left[-\frac{1}{2} \left(\frac{z^2-2\rho zw + w^2}{1-\rho^2}\right)\right]\]

So if the correlation \(\rho = 0\), this simplifies to: \[f(z,w) = \frac{1}{2\pi} \exp \left[-\frac{1}{2} \left({z^2 + w^2}\right)\right] \]

\[f(z,w) = \frac{1}{\sqrt{2\pi}}\exp \left[-\frac{1}{2}z^2\right]\frac{1}{\sqrt{2\pi}}\exp \left[-\frac{1}{2}w^2\right] = f(z)f(w)\]

What famous result does this help us understand?

For musicians - scales; For mathematicians - exercises!

I enjoyed M347 as an OU student, and hope you find it as intriguing and rewarding as I did!