# 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

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CFA

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- 115.020.40 Reading 9 - Common Probability Distributions to 115.020.40.01 Reading 9 - 1. Basic Definitions