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17: Appendices

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    • 17.1: Appendix A to Applied Probability- Directory of m-functions and m-procedures
      This page covers a range of MATLAB functions and scripts focused on statistical analysis, probability calculations, and random processes. Topics include user-defined functions (m-functions), operations on vectors and matrices, Bayesian probabilities, distribution functions (Poisson, Gaussian), joint distributions, and Markov chains. Specific functions are detailed, facilitating tasks like minterm probability calculations, simulation of card matches, and modeling completion times.
    • 17.2: Appendix B to Applied Probability- some mathematical aids
      This page covers mathematical series and their applications, including geometric and exponential series, sums of powers, and counting problems related to arrangements. It also extends binomial coefficients to real numbers. Additionally, it discusses properties of real-valued functions with additive or multiplicative behavior, establishing expressions for bounded functions and defining countable versus uncountable sets with examples.
    • 17.3: Appendix C- Data on some common distributions
      This page provides an overview of discrete and continuous probability distributions, covering basic properties of random variables, including expectation and variance. It details key discrete distributions like Binomial and Poisson, and continuous distributions such as Normal and Exponential, along with their probability functions and moment-generating functions.
    • 17.4: Appendix D to Applied Probability- The standard normal distribution
      This page covers the cumulative distribution function \(\phi(t)\) for the standard normal distribution, defined by an integral involving \(e^{-\mu^2/2}\). It highlights the symmetry property \(\phi(-t) = 1 - \phi(t)\) and provides tabulated values of \(\phi(t)\) to illustrate how it calculates probabilities for standard normal variables.
    • 17.5: Appendix E to Applied Probability - Properties of Mathematical Expectation
      This page covers key properties and theorems related to expectations in probability theory, including linearity, positivity, and monotonicity. It discusses inequalities like Jensen's and Hölder's, along with conditions for integrability such as Fatou's lemma and the dominated convergence theorem.
    • 17.6: Appendix F to Applied Probability- Properties of conditional expectation, given a random vector
      This page covers the conditions and properties of conditional expectations in probability theory. Key concepts include the defining conditions and linearity of conditional expectations, positivity, monotonicity, the law of total probability, and independence. Additionally, it explores monotone convergence, countable additivity, the triangle inequality, Jensen's inequality, and bounds on differences between conditional expectations.
    • 17.7: Appendix G to Applied Probability- Properties of conditional independence, given a random vector
      This page explains conditional independence of random variables, introducing notation and a formal definition for independence given another variable set. It outlines 16 equivalent conditions for this concept and discusses its implications on relationships among random variables, emphasizing the properties that emerge when combining these variables. Overall, it aims to provide a thorough understanding of conditional independence in probability theory.
    • 17.8: Matlab files for "Problems" in "Applied Probability"
      This page provides data entries for probability-related problems using logical variables A, B, C, and D, detailing discrete variables and their probabilities. It includes specific logical combinations to be analyzed using functions like 'mintable' and 'mincalc'. Additionally, data related to numerical methods is presented, with unique codes identifying problems that include matrices for transition and probability distributions, organized for computational tasks in probability and statistics.

    This page titled 17: Appendices was last modified on Sun, 25 Oct 2026 20:34:13 GMT and is shared under a CC BY 3.0 license and was authored, remixed, and/or curated by Paul Pfeiffer via source content that was edited to the style and standards of the LibreTexts platform.