5.6: Chapter 5 - Key Terms and Symbols
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)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
Authors
"5.6: Chapter 5 - Key Terms and Symbols" by Toros Berberyan, Tracy Nguyen, and Alfie Swan is licensed under CC BY 4.0