4.8: Chapter 4 - 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
Combination: A selection of items where the order does not matter.
Combination Rule: The number of ways to choose \(r\) items from \(n\) distinct items without regard to order.
Complementary events: Complementary events are two outcomes of a probability experiment that are the only two possible outcomes and together make up the entire sample space.
Event: a set of certain outcomes of an experiment that you want to have happen.
Event Space: the set of outcomes that make up an event. The symbol is usually a capital letter.
Experiment: an activity or process that will produce specific outcomes.
Factorial: The product of all positive integers up to a number \(n\).
Fundamental Counting Rule (Multiplication Rule): If one event can occur in \( m \) ways and another in \( n \) ways, then both events can occur in \( m \times n \) ways.
Independent events are events where the occurrence of one does not affect the occurrence of the other.
Law of large numbers: a rule in which, as "n" increases, the relative frequency tends towards the actual probability value.
Mutually exclusive events (disjoint) are events with no outcomes in common.
Outcomes: the result of an experiment.
Permutation: An arrangement of items where the order matters.
Permutation Rule (no repetition): The number of ways to arrange \( r \) items from \( n \) distinct items.
Permutation with Repetition: Used when some items are repeated.
Probability: the measure of how likely an event is to occur.
Sample Space: a collection of all possible outcomes of the experiment. It is denoted as SS.
Key Terms
\( _nC_r \) - number of combinations (n choose r).
\( E, X, A, B \) - events (subsets of the sample space).
\( \bar{E} \) - complement of event \( E \).
\( ! \) - factorial symbol (e.g., \( n! \)).
\( n \) - total number of items.
\( n! \) - factorial of \( n \).
\( _nP_r \) - number of permutations (arrangements of \( r \) items from \( n \)).
\( P(E) \) - probability that event \( E \) occurs.
\( P(\bar{E}) \) - probability that event \( E \) does not occur.
\( P(B \mid A) \) - conditional probability of \( B \) given \( A \).
\( r \) - number of items selected.
\( SS \) - sample space (the set of all possible outcomes).
Authors
"4.8: Chapter 4 - Key Terms and Symbols" by Toros Berberyan, Tracy Nguyen, and Alfie Swan is licensed under CC BY 4.0