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Solutions for Chapter 1.7: Introduction to Probability

Probability and Statistics | 4th Edition | ISBN: 9780321500465 | Authors: Morris H. DeGroot, Mark J. Schervish

Full solutions for Probability and Statistics | 4th Edition

ISBN: 9780321500465

Probability and Statistics | 4th Edition | ISBN: 9780321500465 | Authors: Morris H. DeGroot, Mark J. Schervish

Solutions for Chapter 1.7: Introduction to Probability

Probability and Statistics was written by and is associated to the ISBN: 9780321500465. Chapter 1.7: Introduction to Probability includes 11 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Probability and Statistics, edition: 4. Since 11 problems in chapter 1.7: Introduction to Probability have been answered, more than 15132 students have viewed full step-by-step solutions from this chapter.

Key Statistics Terms and definitions covered in this textbook
  • a-error (or a-risk)

    In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).

  • Alias

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

  • Average

    See Arithmetic mean.

  • 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.

  • Causal variable

    When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

  • Center line

    A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.

  • Components of variance

    The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.

  • Conditional probability

    The probability of an event given that the random experiment produces an outcome in another event.

  • Conditional probability distribution

    The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables

  • Contingency table.

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

  • Correlation

    In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.

  • Counting techniques

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

  • Cumulative normal distribution function

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

  • Dependent variable

    The response variable in regression or a designed experiment.

  • Discrete distribution

    A probability distribution for a discrete random variable

  • 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.

  • Generating function

    A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function

  • Goodness of fit

    In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.

  • Hat matrix.

    In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .

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