Random Variables and Probability Distributions

These flashcards cover key vocabulary and concepts related to random variables and probability distributions.

Probability

The chance that something of interest will happen, expressed as a proportion from 0 to 1.

Random Experiment

An experiment that gives different outcomes when repeated under similar conditions.

Random Variable

A variable whose value depends on the outcome of a random experiment.

Discrete Random Variable

Variables that have a finite or countable number of possible values.

Continuous Random Variable

Variables that can take on any value in some interval, leading to an infinite number of possible values.

Probability Mass Function (PMF)

The probability of the random variable X assuming a particular value x, denoted by P(X=x) = P(x).

Cumulative Distribution Function (CDF)

A function that represents the probability that a random variable X will take a value less than or equal to x.

Mean (Expected Value)

The average value that we would expect for a random variable X when performing the random experiment many times.

Variance

A measure of the extent to which the values of a random variable are spread around the mean.

Standard Deviation

The positive square root of the variance, indicating how much the values of a random variable deviate from the mean.

Binomial Distribution

A distribution of a discrete random variable that results from a fixed number of independent Bernoulli trials.

Poisson Distribution

A probability distribution that describes the number of events occurring in a fixed interval of time or space.

Probability Density Function (PDF)

A mathematical function describing the likelihood of a continuous random variable taking on a particular value.

Normal Distribution

A symmetrical, bell-shaped probability distribution defined by its mean and standard deviation.

Standard Normal Distribution

A normal distribution with a mean of 0 and standard deviation of 1.

Independent Events

Two events A and B that have no effect on the occurrence of each other.

Joint Probability

The probability of the occurrence of two or more events simultaneously.

Complementary Events

Two events A and Ā that are mutually exclusive; the occurrence of one excludes the occurrence of the other.

Mutually Exclusive Events

Events that cannot occur at the same time.

Empirical Probability

A probability calculated based on experimental data rather than theoretical considerations.

Counting Principles

Principles used to calculate the number of ways to choose or arrange items, including permutations and combinations.