Random Variables & Discrete Probability Distribution

This set of vocabulary flashcards covers the fundamental concepts of random variables, including discrete and continuous types, specific distributions like Binomial and Poisson, and counting principles like permutations and combinations.

Categorical Variable

Variables that take category or label values and are non-numerical or qualitative, such as flower color or shape of leaves.

Numerical Variable

Measurable or countable quantitative variables such as plant height, fruit weight, or number of petals.

Random Variable

A variable whose value is determined by a random experiment, random trial, sample, or simulation, providing a numerical description of the outcome.

Discrete Random Variable

A type of random variable that takes on only a finite or countable number of distinct values, such as the number of children in a family.

Continuous Random Variable

A type of random variable that takes an infinite number of possible values within an interval, usually representing measurements like height, weight, or time.

Probability Distribution

A list, table, or equation showing all possible values of a discrete random variable together with their associated probabilities.

Probability Mass Function

A function used to represent the distribution of a discrete random variable.

Probability Histogram

A graphical display of sample values where the horizontal axis represents the range of values and the vertical axis represents the frequency or relative frequency.

Expected Value ($E(X)$)

Also denoted as the mean ($\mu$), it represents the average outcome of the possible values for a given data generating process.

Standard Deviation ($sd(X)$)

The degree to which the values of a random variable differ from the expected value, defined as the square root of the variance.

Binomial Distribution

A probability distribution appropriate for sampling in an infinitely large population where there are $n$ identical trials, each with only two possible outcomes (success or failure).

Bernoulli Trial

A single repetition of a binomial experiment, named after Jacob Bernoulli.

Permutation

The act of arranging members of a set into a sequence or order where the order or sequence is important.

Combination

A way of selecting items from a collection such that the order of selection does not matter.

Poisson Distribution

A discrete probability distribution named after Simeon Denis Poisson that shows how many times an event is likely to occur within a specified period of time at a constant rate.

Poisson Approximation to the Binomial

A method where a binomial distribution with a large $n$ and small $p$ is approximated by a Poisson distribution with parameter $\mu = n \times p$.