Chapter 2 - Random Variables

Question 1

Describe a probability mass function (PMF).

Answer 1

A PMF is a mathematical function used to precisely describe the values of random variables. Denoted as fx(x)
The PMF returns the probability that a discrete random variable takes a certain value (shown as x)
The PMF is a discrete function.

Question 2

What are the two properties a PMF must have?

Answer 2

The value returned from a PMF must be non-negative
The sum across all values in the support of a random variable must be one (1).

Question 3

Describe a cumulative distribution function (CDF)

Answer 3

The CDF measures the total probability of observing a value less than or equal to a given value (or the input x). Denoted as Fx(x).
(i.e. Pr(X [greater than or equal to x))
The CDF is a continuous function (it can support any value of x).

Question 4

What is the relationship between the PMF and CDF?

Answer 4

The CDF can always be expressed as the sum of the PMF for all values in the support that are less than or equal to x.

The PMF is the difference of the CDFs evaluated at consecutie values in the support of X.