- 5.8.1E: If X is a random variable with mean 33 and variance 16, use Chebysh...
- 5.8.2E: If E(X) = 17 and E(X2) = 298, use Chebyshev’s inequality to determi...
- 5.8.3E: Let X denote the outcome when a fair die is rolled. Then ? = 7/2 an...
- 5.8.4E: If the distribution of Y is b(n, 0.5), give a lower bound for P(|Y/...
- 5.8.5E: If the distribution of Y is b(n, 0.25), give a lower bound for P(|Y...
- 5.8.6E: Let be the mean of a random sample of size n = 15 from a distributi...
- 5.8.7E: Suppose that W is a continuous random variable with mean 0 and a sy...
- 18.104.22.168-1: If X is a random variable with mean 33 and variance 16, use Chebysh...
- 22.214.171.124-2: If E(X) = 17 and E(X2) = 298, use Chebyshevs inequality to determin...
- 126.96.36.199-3: Let X denote the outcome when a fair die is rolled. Then = 7/2 and ...
- 188.8.131.52-4: If the distribution of Y is b(n, 0.5), give a lower bound for P(|Y/...
- 184.108.40.206-5: If the distribution of Y is b(n, 0.25), give a lower bound for P(|Y...
- 220.127.116.11-6: Let X be the mean of a random sample of size n = 15 from a distribu...
- 18.104.22.168-7: Suppose that W is a continuous random variable with mean 0 and a sy...
Solutions for Chapter 5.8: Distributions of Functions of Random Variables
Full solutions for Probability and Statistical Inference | 9th Edition
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.
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.
An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
Bivariate normal distribution
The joint distribution of two normal random variables
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.
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.
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.
The variance of the conditional probability distribution of a random variable.
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.
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.
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).
Defects-per-unit control chart
See U chart
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.
Estimate (or point estimate)
The numerical value of a point estimator.
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.
Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.
In statistical quality control, that portion of a number of units or the output of a process that is defective.
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on