Lecture 3 – Random Variables
by Suraj Rampure (Summer 2020)
Make sure to complete the Quick Check questions in between each video. These are ungraded, but it’s in your best interest to do them.
Formal definition of random variables.
Distributions of random variables.
Defining the Bernoulli and binomial distributions. (Stat 88 reading)
Discussing equality of random variables – equal vs. equal in distribution.
Expectation. Linearity of expectation. Sample calculations, and the expectation of the Bernoulli and binomial distributions.
Variance of random variables. Walking through an alternate calculation of variance. Variance of a linear transformation.
Deriving the variance of a sum. Understanding covariance, correlation, and independence.
Variance of an i.i.d. sum. Variance of the Bernoulli and binomial distributions.
Variability of the sample mean. Reviewing inferential concepts from Data 8, but with the framework of random variables.