Module 7: Discrete Random Variables & Probability Mass Functions

Question 1

what is a random variable?

Answer 1

a real valued function whose domain is a sample space.

Question 2

what is the notation for random variables?

Answer 2

random variable themselves are uppercase letters, X, Y, Z while the actual values are lower case, x, y ,z

This means we generally talk abt “the probability that random variable X takes on the value x”

Question 3

what is a discrete random variable?

Answer 3

a random variable that is takes the form of a finite number or a countably infinite number

Question 4

what is a probability mass function (PmF)?

Answer 4

A discrete random variable has an associated probability function or PmF, denoted by P({X = x}) or simply p(x), that assigns a probability to each numerical value that the random variable can take on. This function satisfies the following conditions:

1. P({X = x}) = p(x) ≥ 0
2. SUM(P({X = x}) = 1, where the sum over all possible values of x