- 6.3.1: The distribution function for the duration of a certain soap opera ...
- 6.3.2: The time it takes for a student to finish an aptitude test (in hour...
- 6.3.3: The mean and standard deviation of the lifetime of a car muffler ma...
- 6.3.4: A random variable X has the density function f (x) = B 3e3x if 0 x ...
- 6.3.5: Find the expected value of a random variable X with the density fun...
- 6.3.6: Let Y be a continuous random variable with probability distribution...
- 6.3.7: Let the probability density function of tomorrows Celsius temperatu...
- 6.3.8: Let X be a continuous random variable with probability density func...
- 6.3.9: A right triangle has a hypotenuse of length 9. If the probability d...
- 6.3.10: Let X be a random variable with probability density function f (x) ...
- 6.3.11: Let X be a random variable with the probability density function f ...
- 6.3.12: Suppose that X, the interarrival time between two customers enterin...
- 6.3.13: For n 1, let Xn be a continuous random variable with the probabilit...
- 6.3.14: Let X be a continuous random variable with the probability density ...
- 6.3.15: Let X be a continuous random variable with density function f . A n...
- 6.3.16: Let X be a continuous random variable with probability density func...
- 6.3.17: Let X be a nonnegative random variable with distribution function F...
- 6.3.18: Let X be a continuous random variable. Prove that . n=1 P ! |X| n "...
- 6.3.19: Let X be the random variable introduced in Exercise 12. Applying th...
- 6.3.20: Suppose that X is the lifetime of a randomly selected fan used in c...
- 6.3.21: Let X be a continuous random variable with probability density func...
Solutions for Chapter 6.3: Expectations and Variances
Full solutions for Fundamentals of Probability, with Stochastic Processes | 3rd Edition
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
Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation
A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study
Asymptotic relative eficiency (ARE)
Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.
A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.
The joint probability distribution of two random variables.
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.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.
In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.
A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.
Cumulative sum control chart (CUSUM)
A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t
Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.
In statistical quality control, that portion of a number of units or the output of a process that is defective.
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .