AP Stats Unit 4

Random Phenomenon

A situation where the outcome is uncertain

Sample Space

The set of all possible outcomes

Event

A subset of the sample space

Probability

A number between 0 and 1 that describes the likelihood of an event occurring

Complement

The event that an event does not occur

Addition Rule

For any two events, P(A or B) = P(A) + P(B) – P(A and B)

Multiplication Rule

For independent events, P(A and B) = P(A) × P(B)

Conditional Probability

The probability of event A given that event B has occurred, denoted P(A|B)

Independent Events

Two events are independent if the occurrence of one does not affect the probability of the other

Random Variable

A variable that takes numerical values determined by the outcome of a random phenomenon

Discrete Random Variable

A random variable that has a finite or countable number of possible values

Continuous Random Variable

A random variable that can take any value in an interval

Probability Distribution

A function that gives the probabilities of a random variable's possible values

Expected Value (Mean)

The average value of a random variable over many repetitions

Variance

The expected value of the squared deviation from the mean

Standard Deviation

The square root of the variance

Binomial Distribution

The probability distribution of the number of successes in a fixed number of independent trials with the same probability of success

Geometric Distribution

The probability distribution of the number of trials needed to get the first success in repeated, independent Bernoulli trial