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Solutions for Chapter 3.3: Law of Total Probability

Fundamentals of Probability, with Stochastic Processes | 3rd Edition | ISBN: 9780131453401 | Authors: Saeed Ghahramani

Full solutions for Fundamentals of Probability, with Stochastic Processes | 3rd Edition

ISBN: 9780131453401

Fundamentals of Probability, with Stochastic Processes | 3rd Edition | ISBN: 9780131453401 | Authors: Saeed Ghahramani

Solutions for Chapter 3.3: Law of Total Probability

Solutions for Chapter 3.3
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Textbook: Fundamentals of Probability, with Stochastic Processes
Edition: 3
Author: Saeed Ghahramani
ISBN: 9780131453401

Fundamentals of Probability, with Stochastic Processes was written by and is associated to the ISBN: 9780131453401. Since 23 problems in chapter 3.3: Law of Total Probability have been answered, more than 12997 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 3.3: Law of Total Probability includes 23 full step-by-step solutions. This textbook survival guide was created for the textbook: Fundamentals of Probability, with Stochastic Processes, edition: 3.

Key Statistics Terms and definitions covered in this textbook
  • Backward elimination

    A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain

  • Binomial random variable

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

  • Categorical data

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

  • Central tendency

    The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.

  • Confounding

    When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.

  • Control limits

    See Control chart.

  • Correction factor

    A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

  • Critical region

    In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

  • Cumulative normal distribution function

    The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.

  • Defect concentration diagram

    A quality tool that graphically shows the location of defects on a part or in a process.

  • Dependent variable

    The response variable in regression or a designed experiment.

  • Discrete random variable

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

  • Distribution free method(s)

    Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).

  • Error mean square

    The error sum of squares divided by its number of degrees of freedom.

  • Estimate (or point estimate)

    The numerical value of a point estimator.

  • Exhaustive

    A property of a collection of events that indicates that their union equals the sample space.

  • Expected value

    The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

  • Extra sum of squares method

    A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.

  • Gamma function

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

  • Geometric random variable

    A discrete random variable that is the number of Bernoulli trials until a success occurs.

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