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Solutions for Chapter 8: Bayesian Statistical Inference

Introduction to Probability, | 2nd Edition | ISBN: 9781886529236 | Authors: Dimitri P. Bertsekas John N. Tsitsiklis

Full solutions for Introduction to Probability, | 2nd Edition

ISBN: 9781886529236

Introduction to Probability, | 2nd Edition | ISBN: 9781886529236 | Authors: Dimitri P. Bertsekas John N. Tsitsiklis

Solutions for Chapter 8: Bayesian Statistical Inference

Solutions for Chapter 8
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Textbook: Introduction to Probability,
Edition: 2
Author: Dimitri P. Bertsekas John N. Tsitsiklis
ISBN: 9781886529236

This textbook survival guide was created for the textbook: Introduction to Probability,, edition: 2. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 8: Bayesian Statistical Inference includes 24 full step-by-step solutions. Introduction to Probability, was written by and is associated to the ISBN: 9781886529236. Since 24 problems in chapter 8: Bayesian Statistical Inference have been answered, more than 9222 students have viewed full step-by-step solutions from this chapter.

Key Statistics Terms and definitions covered in this textbook
  • Additivity property of x 2

    If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.

  • Alias

    In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

  • Alternative hypothesis

    In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test

  • Binomial random variable

    A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.

  • Bivariate distribution

    The joint probability distribution of two random variables.

  • Bivariate normal distribution

    The joint distribution of two normal random variables

  • Categorical data

    Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

  • Chi-square (or chi-squared) random variable

    A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.

  • Comparative experiment

    An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.

  • Completely randomized design (or experiment)

    A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.

  • Conditional probability mass function

    The probability mass function of the conditional probability distribution of a discrete random variable.

  • Contingency table.

    A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria

  • Convolution

    A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.

  • Correlation coeficient

    A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).

  • Counting techniques

    Formulas used to determine the number of elements in sample spaces and events.

  • Discrete random variable

    A random variable with a inite (or countably ininite) range.

  • Discrete uniform random variable

    A discrete random variable with a inite range and constant probability mass function.

  • Fixed factor (or fixed effect).

    In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.

  • Gamma function

    A function used in the probability density function of a gamma random variable that can be considered to extend factorials

  • Gaussian distribution

    Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications

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