Probability (frequentist interpretation): the proportion of times he event occurs in independent repitions of the random experiment in the long run

Equally likely framework (classical probability): any individual outcome is equally likely to occur

• for example, when rolling a fair die, each of the six outcomes are equally likely
• $P(event) = \frac{Number \space of ways \space the \space event \space can \space happen}{Total \space number \space of \space things \space that \space can \space happen}$

If events $A$ and $B$ are mutually exclusive (disjoint), they cannot both occur simultaneously, and

• $P(A \space or \space B) = P(A) + P(B)$

If events $C$ and $D$ are independent, they are uninformative about each other, and

• $P(C \space and \space D) = P(C) \times P(D)$

Random Variable (r.v.): a numerical variable resulting from a random experiment (we assign numbers to each outcome, typically using some kind of rule)

• Discrete and Continous variables
• Typically use a captial letter (like $X$) to refer to definition of the r.v. itself, while the corresponding lower-case letter (like $x$) refers to individual values of the r.v.

Discrete Random Variable: outcomes are limited to a countable/listable set of real numbers (can think of the “next” possible value)

Support: the possible values a r.v. can take

Probability Mass Function (PMF): decribesthe probabilities associated with each possible value of a discrete r.v.

• $f(x) = P(X = x)$
• This and its continuous random variable counterpart are often called a r.v.’s distribution