Houjun Liu

random variable

A random variable is a variable that has a value, but there are uncertainty with respect to what that value is.

  • discrete: finite number of values
  • continuous: infinitely many possible values

probability mass function

A discrete random variable is encoded as a probability mass function

probability density function

A continuous random variable is represented as a probability density function.

summary statistics

adding random variables

“what’s the probability of \(X + Y = n\)”?

\begin{equation} \sum_{i=0}^{n} P(X=i, Y=n-i) \end{equation}

for every single outcome, we want to create every possible operation which causes the two variables to sum to \(n\).