# 1. Basic Definitions

## a. define a probability distribution and distinguish between discrete and continuous random variables and their probability functions;

## b. describe the set of possible outcomes of a specified discrete random variable;

What is a probability distribution?

A probability distribution specifies the probabilities of the possible outcomes of a random variable.

What is a discrete probability distribution?

- The discrete probability distribution is a table, graph, or rule that associates the probability of something happening with each possible input variable.

- `P(X=x_i)`

< a probability for each possible value of `x_i`

What is a discrete variable? What is a continuous variable?

- A discrete variable is a value that can only assume some fixed set of values. E.g., a rating from 1-5 (you can't answer 1.4), answers correct out of 10 (you can't get 7.2 answers correct), number of movies you saw this year.

- A continuous variable is one that can take on any value and the number of possible values can't be counted. Height, speed, most measurements b/c you could get very granular with the measurement.

What two things do you want to know about any random variable in order to get a probability distribution?

1. The list of all possible values that the random variable can take on (range)

2. The probability of each value occurring

##### Source:

- CFA