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
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