Random Variables & Probability Models

Flashcards related to Random Variables and Probability Models, covering definitions and key concepts.

Random Variable

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

Discrete Random Variable

A random variable that has a finite number of values, represented as isolated points on the number line.

Continuous Random Variable

A random variable that can take on any value in an interval of numbers on the number line.

Probability Distribution

A mathematical description of a random phenomenon consisting of each possible outcome and the probabilities assigned to each outcome.

Mean (Expected Value)

A measure of the central tendency of a random variable, calculated as the sum of all possible values weighted by their probabilities.

Standard Deviation

A measure of the amount of variation or dispersion in a set of values; for a discrete random variable, it's denoted as σ.

Variance

The expectation of the squared deviation of a random variable from its mean, denoted as σ².

Binomial Distribution

The distribution of the count X of successes in a binomial setting with parameters n (number of observations) and p (probability of success).

Parameters of Binomial Distribution

In a binomial distribution, parameters n (number of trials) and p (probability of success) are used to define the distribution.

Binomial Random Variable

The count of successful outcomes of a binomial experiment, usually denoted as X.

Probability of Success (p)

The probability of a successful outcome in a single trial within a binomial distribution.

Probability of Failure (q)

The probability of failure in a single trial within a binomial distribution, calculated as q = 1 - p.

Binomial Coefficient

The number of ways to choose k successes from n trials, denoted as nCk.

Mean of Binomial Distribution

Calculated as μx = np, where n is the number of trials and p is the probability of success.

Standard Deviation of Binomial Distribution

Calculated as σx = √(np(1-p)), where n is the number of trials and p is the probability of success.