Fundamentals of probability with stochastic processes answers

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• Acceptance region

  In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion

• All possible (subsets) regressions

  A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions

• 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

• Biased estimator

  Unbiased estimator.

• Bivariate normal distribution

  The joint distribution of two normal random variables

• Box plot (or box and whisker plot)

  A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).

• Cause-and-effect diagram

  A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

• 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.

• Conditional probability mass function

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

• 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.

• Conidence level

  Another term for the conidence coeficient.

• Contingency table.

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

• Contour plot

  A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

• Counting techniques

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

• Cumulative distribution function

  For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

• Deining relation

  A subset of effects in a fractional factorial design that deine the aliases in the design.

• Discrete random variable

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

• Factorial experiment

  A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.

• Gamma random variable

  A random variable that generalizes an Erlang random variable to noninteger values of the parameter r

• Harmonic mean

  The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .

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