5.6: Chapter 5 - Key Terms and Symbols

Statistics C1000: Introduction to Statistics · LibreTexts

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    Glossary of Key Terms and Symbols

    Key Terms

    Binomial Probability: The probability of obtaining a specific number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure).

    Binomial Probability Distribution: A discrete probability distribution that represents the number of successes in a set number of identical and independent trials, with the same probability of success for each trial.

    Continuous Variable: A variable that can take on an infinite number of possible values within a given range. These values are measurable, not countable (e.g., height, time, temperature).

    Discrete Probability Distribution: A listing or function that shows the probabilities of all possible values of a discrete random variable, with each probability between 0 and 1 and the total adding up to 1.

    Discrete Variable: A variable that can only take on specific, separate values, usually whole numbers that can be counted (e.g., number of books, number of people).

    Expected Value: The theoretical average of a random variable, representing the long-term outcome if the experiment is repeated many times.

    Mean: The average value of a discrete probability distribution, calculated by considering the weighted sum of all possible values.

    Probability Distribution: A function or list that shows the likelihood of each possible outcome of a random variable.

    Random Variable: A variable whose value is determined by the outcome of a random event or experiment. It can be either discrete or continuous.

    Standard Deviation: A measure that describes how spread out the values of a probability distribution are around the mean.

    Variance: The average of the squared differences between each value and the mean, indicating the level of dispersion in a distribution.

    Key Symbols

    \( X \): Random variable

    \( P(X) \): Probability of the random variable \( X \) taking on a specific value

    \( E(X) \): Expected value (mean) of the random variable \( X \)

    \( \mu \): Population mean (same as \( E(X) \) for theoretical distributions)

    \( \sigma^2 \): Variance of a probability distribution

    \( \sigma \): Standard deviation of a probability distribution

    \( n \): Number of trials in a binomial experiment

    \( p \): Probability of success in a single trial

    \( q \): Probability of failure in a single trial (where \( q = 1 - p \))

    \( X\): Number of successes (often used in binomial probability)

    \( \sum \): Summation symbol, indicating the sum over all values

    This page titled 5.6: Chapter 5 - Key Terms and Symbols was last modified on Wed, 13 Aug 2025 01:13:49 GMT and is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Toros Berberyan, Tracy Nguyen, and Alfie Swan.