On Monday this week we will talk about Bayes rule, or how we should update our beliefs based on new information. On Wednesday we will review expected value, variance, and standard deviation of random variables, as well as the normal distribution.

In-class activities, case studies, exercises, etc for this week

We will work on these in breakout rooms. I suggest having one person share their screen and serve as note-taker, or quickly sharing a Google doc so you can work together. All the activities will be a component of the homework you hand in next week.

Activity 1 (Monday): Discuss among your groups the difference between a prior probability $P(A)$ and a posterior probability $P(A\mid B)$. Come up with three examples of events $A$ and $B$ that illustrate how $P(A)$ differs from $P(A\mid B)$. Note that up to date, we have called the former simply a “marginal” probability and the latter a “conditional” probability. These are still valid labels, but prior and posterior (i.e., after seeing data or evidence) are more descriptive here. For your examples, how does the joint probability $P(A,B)$ differ from $P(A)$ and $P(A\mid B)$? No more than one should be from your readings.

Activity 2 (Monday): Work through the facial recognition case study. See this (optional) follow up video, documenting a real case where police misused facial recognition software to affect a wrongful arrest

Materials for Wednesday:

• Expected value, variance, standard deviation
• Continuous random variables & the normal distribution (R script)

Some reference materials used in class this week

You may find these links helpful for our activities; see also the material on last week’s post.

Monday:

• Bayes Rule

Wednesday:

• Probability Models page 181-184 and the subsection “The normal distribution” on p 194-202

Readings, videos, and activities to do for next week

For Monday, please read Finding anomalies (hypothesis testing)

For Wednesday, please read Data exploration and work through the following R walkthroughs:

• Exploring city temperatures in San Diego and Rapid City
• Test scores and GPAs for UT undergrads

Don’t just read these walkthroughs, you should actually make sure you can run the code on your computer and understand the output. Otherwise you will quickly get behind!

You may also find the following videos helpful:

• Measuring variation in categorical and numerical variables
• Boxplots and dotplots for measuring relationships between categorical and numerical variables.
• Scatter plots, correlation, and multivariate plots.

Exercises and other things due next week

Complete the activities above, and these takehome exercises