Random Variables

Random Variables

We use capital letters like $X, Y$ to denote these.

When to use capitals vs. lowercase

Typically the convention is to use upper case letter when using probabilities outside of algebra (not substituting numbers):

P (X = 1), E (X), . . .

while when we'd plug in and do algebra on numbers, they get the lower case:

σ_{X} = \sum_{i = 1}^{n} (x_{i} - μ_{X})^{2} p (x)

Example

A person's visit to a nonprofit organization's website can be considered as success $S$ if a donation is made and a failure $F$ otherwise. $S = {S, F}$ , define an random variable $X$ by $X (S) = 1$ and $X (F) = 0$ . The random variable $X$ indicates whether (1) or (0), so whether a donation was made.

Bernoulli Random Variable

Any random variable whose only possible values are 0, 1 is called a Bernoulli Random Variable.