Review of Module 4 of Data Analysis for Social Scientists (MITx, edX) – Functions and Moments of Random Variables and Intro to Regressions
I must say that I struggled with this module. There were theorems and equations that my rusty mathematics brain took time to process. Yet my current workload doesn’t afford me the patience to grasp the concepts in depth. (I’m not offering it as an excuse, just context). I mean, just try to get a handle of this:
- Law of iterated expectations: The expectation of the expectation of Y given X is equal to the expectation of Y
- Law of total variance: The variance of Y is equal to the variance of the expectation of Y given X added to the expectation of the variance of Y given X
(To be fair, it’s easier to understand by writing the equation.)
My sad score for the ‘Functions of Random Variables’ section
But at least, I think, I got the general gist. Much of the module was about transforming random variables and deriving their probability distribution functions (PDF), followed by calculating moments (i.e. mean, median, mode). At the end Sarah gave an introduction to covariance/correlation, and the link between probability, random variables and data analysis is getting clearer.