- 5-3.5-34: Determine the value of c such that the function f(x, y) cxy for 0 x...
- 5-3.5-35: 5-35. Continuation of Exercise 5-34. Determine the following: (a) (...
- 5-3.5-36: Continuation of Exercise 5-34. Determine the following: (a) Margina...
- 5-3.5-37: 5-37. Determine the value of c that makes the function f(x, y) c(x ...
- 5-3.5-38: Continuation of Exercise 5-37. Determine the following: (a) (b) (c)...
- 5-3.5-39: 5-39. Continuation of Exercise 5-37. Determine the following: (a) M...
- 5-3.5-40: Determine the value of c that makes the function f(x, y) cxy a join...
- 5-3.5-41: Continuation of Exercise 5-40. Determine the following:
- 5-3.5-42: Continuation of Exercise 5-40. Determine the following: (a) Margina...
- 5-3.5-43: Determine the value of c that makes the function a joint probabilit...
- 5-3.5-44: Continuation of Exercise 5-43. Determine the following: (a) (b) (c)...
- 5-3.5-45: 5-45. Continuation of Exercise 5-43. Determine the following: (a) M...
- 5-3.5-46: Determine the value of c that makes the function a joint probabilit...
- 5-3.5-47: Continuation of Exercise 5-46. Determine the following:
- 5-3.5-48: Continuation of Exercise 5-46. Determine the following: (a) Margina...
- 5-3.5-49: 5-49. Two methods of measuring surface smoothness are used to evalu...
- 5-3.5-50: Continuation of Exercise 5-49. Determine the following:
- 5-3.5-51: 5-51. Continuation of Exercise 5-49. Determine the following: (a) M...
- 5-3.5-52: The time between surface finish problems in a galvanizing process i...
- 5-3.5-53: 5-53. A popular clothing manufacturer receives Internet orders via ...
- 5-3.5-54: The conditional probability distribution of Y given X x is for y 0 ...
Solutions for Chapter 5-3: TWO CONTINUOUS RANDOM VARIABLES
Full solutions for Applied Statistics and Probability for Engineers | 3rd Edition
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
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
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.
Chi-square (or chi-squared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.
Coeficient of determination
See R 2 .
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.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
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.
The amount of variability exhibited by data
Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.
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.
Estimator (or point estimator)
A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.
A property of a collection of events that indicates that their union equals the sample space.
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 series of tests in which changes are made to the system under study
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.
Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on
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 .