# Day 61: The Challenges of Combining Random Variables

In AP Stats, we’ve begun our study of how random variables can be combined.  I use a very simple partner activity to get students thinking about what we can and can’t do when combining random variables.

APS 6.2 – Day 2 Combining Random Variables Partner Activity

Through doing the first part of the activity, I found some students didn’t actually understand that the term “probability distribution” meant to create the table with the random variable, X, and their related probability values.  They were just writing out what the probabilities were.  Also, determining the standard deviation from a probability distribution was still elusive.  So we spent some time reviewing the formula followed by how to use the calculator to make the calculations easier.  (Sorry, forgot to take photos today ;{

I’m worried that my kiddos lost sight of the purpose of the activity in the process of completing the calculations.  We did finish the questions for the combined random variable X + Y; yet I am very sure that the conceptual understanding is missing.  So on block day Wednesday, we’ll revisit the reasons behind the calculation of the standard deviation using a simplified version of  Dave Bock (of Cornell University)’s AP article entitled, Why Variances Add–And Why It Matters.  We’ll talk about his coined phrase “Pythagorean Theorem of Statistics” as well as explore his three questions:

1. Why do we add the variances?
2. Why do we add even when working with the difference of the random variables?
3. Why do the variables have to be independent?

We’ll then look at one of the Math XL homework questions:

followed by having my students look at the work they did for the combined random variable X – Y on the Partner Activity.  Wednesday will be a busy day, and luckily we have 90 minutes to fortify their understanding.  Keeping my fingers crossed.