Statistics 2 Lecture Notes

This set of flashcards covers key concepts and definitions related to the Statistics 2 course, focusing on probability theory, distributions, and statistical measures.

Probability

A numerical measure that describes how likely an event is to occur, quantifying uncertainty from 0 (impossible) to 1 (certain).

Random Experiment

An experiment that has at least two possible outcomes and is characterized by uncertainty regarding which outcome will occur.

Sample Space

The collection of all possible outcomes of an experiment, denoted by S.

Event

Any subset of the sample space, consisting of one or more outcomes.

Complement Rule

States that the probability of an event not occurring is equal to one minus the probability that the event occurs.

Addition Rule

Used to compute the probability that at least one of two events occurs; it varies based on whether the events are mutually exclusive.

Multiplication Rule

Used to compute the probability that two or more events occur simultaneously, applicable in both independent and dependent scenarios.

Conditional Probability

The probability that an event occurs given that another event has already occurred.

Discrete Random Variable

A random variable that can assume only specific, separated values.

Continuous Random Variable

A random variable that can assume an infinite number of values within a given interval.

Mean (Expected Value)

The average value of a probability distribution, representing a typical or central value.

Variance

A measure of how much the values of a random variable vary around the mean.

Standard Deviation

The positive square root of the variance, providing a measure of spread or variability.

Binomial Distribution

A discrete probability distribution that describes the number of successes in a fixed number of independent trials, each with the same probability of success.

Poisson Distribution

A discrete probability distribution used to model the number of events occurring in a fixed interval of time or space.

Normal Distribution

A continuous probability distribution characterized by its bell-shaped curve, defined by its mean and standard deviation.

Standard Normal Distribution (Z-Distribution)

A normal distribution with a mean of 0 and a standard deviation of 1, used to standardize scores.

Empirical Rule

States that for a normal distribution, approximately 68% of values lie within one standard deviation of the mean, 95% lie within two standard deviations, and 99.7% lie within three.

Probability Density Function (PDF)

A function that describes the likelihood of a continuous random variable taking on a particular value, defining the shape of the distribution.

Mean of Uniform Distribution

The average of the minimum and maximum values, calculated as bc = (a + b) / 2.

Variance of Uniform Distribution

Calculated as c3² = (b - a)² / 12, representing how spread out the values are.