- 7.7.1: Let X be a random variable with probability f(x)=1 3,x=1 ,2,3, 0, e...
- 7.7.2: Let X be a binomial random variable with probability distribution f...
- 7.7.3: Let X1 and X2 be discrete random variables withthe joint multinomia...
- 7.7.4: Let X1 and X2 be discrete random variables with joint probability d...
- 7.7.5: Let X have the probability distribution f(x)=1, 0 <x<1, 0, elsewher...
- 7.7.6: Given the random variable X with probability distribution f(x)=2x, ...
- 7.7.7: The speed of a molecule in a uniform gas at equilibrium is a random...
- 7.7.8: A dealers prot, in units of $5000, on a new automobile is given by ...
- 7.7.9: The hospital period, in days, for patients following treatment for ...
- 7.7.10: The random variables X and Y , representing the weights of creams a...
- 7.7.11: The amount of kerosene, in thousands of liters, in a tank at the be...
- 7.7.12: Let X1 and X2 be independent random variables each having the proba...
- 7.7.13: A current of I amperes owing through a resistance of R ohms varies ...
- 7.7.14: Let X be a random variable with probability distribution f(x)=1+x 2...
- 7.7.15: Let X have the probability distribution f(x)=2(x+1) 9 , 1 <x<2, 0, ...
- 7.7.16: Show that the rth moment about the origin of the gamma distribution...
- 7.7.17: A random variable X has the discrete uniform distribution f(x;k)=1 ...
- 7.7.18: A random variable X has the geometric distribution g(x;p)=pqx1 for ...
- 7.7.19: A random variable X has the Poisson distribution p(x;)=ex/x! forx =...
- 7.7.20: The moment-generating function of a certain Poisson random variable...
- 7.7.21: Show that the moment-generating function of the random variable X h...
- 7.7.22: Using the moment-generating function of Exercise 7.21, show that th...
- 7.7.23: If both X and Y , distributed independently, follow exponential dis...
- 7.7.24: By expanding etx in a Maclaurin series and integrating term by term...
Solutions for Chapter 7: Fundamental Sampling Distributions and Data Descriptions
Full solutions for Probability and Statistics for Engineers and the Scientists | 9th Edition
Solutions for Chapter 7: Fundamental Sampling Distributions and Data DescriptionsGet Full Solutions
Summary of Chapter 7: Fundamental Sampling Distributions and Data Descriptions
Focus on sampling from distributions or populations and study such important quantities as the sample mean and sample variance, which will be of vital importance.
2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.
2 k p - factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each
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.
An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.
Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data
The probability of an event given that the random experiment produces an outcome in another event.
Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.
A probability distribution for a continuous random variable.
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
Formulas used to determine the number of elements in sample spaces and events.
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
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
Error sum of squares
In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a model-itting process and not on replication.
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.
A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications
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 .