Houjun Liu

SU-CS109 NOV102023

Key Sequence


New Concepts

Important Results / Claims

Review: expectation. Expectation of the sums of random variables are linear regardless of whether or not the variables are IID, independent, whatever.

“expectation of the sum is the sum of the expectations”. “Can I write the expectation I want to calculate as the sum of something else?”


Interesting Factoids

\(\mathbb{E}[Y]\) =

  • \(x=1\): 3
  • \(x=2\): 5 + Y
  • \(x=3\): 7 + Y

\begin{equation} \mathbb{E}[Y] = 3 \cdot \frac{1}{3} + (5+ \mathbb{E}[Y]) \cdot \frac{1}{3} + (7+ \mathbb{E}[Y]) \cdot \frac{1}{3} \end{equation}