 5.5.1: Let X be a random variable with probability densityfunction (a) Wha...
 5.5.2: A system consisting of one original unit plus aspare can function f...
 5.5.3: Consider the functionf (x) =0C(2x x3) 0 < x < 520 otherwiseCould f ...
 5.5.4: The probability density function of X, the lifetimeof a certain typ...
 5.5.5: A filling station is supplied with gasoline once aweek. If its week...
 5.5.6: Compute E[X] if X has a density function given by
 5.5.7: The density function of X is given by If E[X] = 35, find a and b.
 5.5.8: The lifetime in hours of an electronic tube is a randomvariable hav...
 5.5.9: Consider Example 4b of Chapter 4, but now supposethat the seasonal ...
 5.5.10: Trains headed for destination A arrive at the trainstation at 15mi...
 5.5.11: A point is chosen at random on a line segmentof length L. Interpret...
 5.5.12: A bus travels between the two cities A and B,which are 100 miles ap...
 5.5.13: You arrive at a bus stop at 10 oclock, knowingthat the bus will arr...
 5.5.14: Let X be a uniform (0, 1) random variable. ComputeE[Xn] by using Pr...
 5.5.15: If X is a normal random variable with parameters = 10 and 2 = 36, c...
 5.5.16: The annual rainfall (in inches) in a certain region isnormally dist...
 5.5.17: A man aiming at a target receives 10 points if hisshot is within 1 ...
 5.5.18: Suppose that X is a normal random variable withmean 5. If P{X > 9} ...
 5.5.19: Let X be a normal random variable with mean12 and variance 4. Find ...
 5.5.20: If 65 percent of the population of a large communityis in favor of ...
 5.5.21: Suppose that the height, in inches, of a 25yearoldman is a normal...
 5.5.22: The width of a slot of a duralumin forging is (ininches) normally d...
 5.5.23: One thousand independent rolls of a fair die willbe made. Compute a...
 5.5.24: The lifetimes of interactive computer chips producedby a certain se...
 5.5.25: Each item produced by a certain manufacturer is,independently, of a...
 5.5.26: Two types of coins are produced at a factory: a faircoin and a bias...
 5.5.27: In 10,000 independent tosses of a coin, the coinlanded on heads 580...
 5.5.28: Twelve percent of the population is left handed.Approximate the pro...
 5.5.29: A model for the movement of a stock supposesthat if the present pri...
 5.5.30: An image is partitioned into two regions, onewhite and the other bl...
 5.5.31: (a) A fire station is to be located along a road oflength A,A < q. ...
 5.5.32: The time (in hours) required to repair a machine isan exponentially...
 5.5.33: The number of years a radio functions is exponentiallydistributed w...
 5.5.34: Jones figures that the total number of thousandsof miles that an au...
 5.5.35: The lung cancer hazard rate (t) of a tyearoldmale smoker is such ...
 5.5.36: Suppose that the life distribution of an item has thehazard rate fu...
 5.5.37: If X is uniformly distributed over (1, 1), find(a) P{X > 12};(b) ...
 5.5.38: If Y is uniformly distributed over (0, 5), whatis the probability t...
 5.5.39: If X is an exponential random variable withparameter = 1, compute t...
 5.5.40: If X is uniformly distributed over (0, 1), find thedensity function...
 5.5.41: Find the distribution of R = Asin , where A isa fixed constant and ...
Solutions for Chapter 5: First Course in Probability 8th Edition
Full solutions for First Course in Probability  8th Edition
ISBN: 9780136033134
Solutions for Chapter 5
Get Full SolutionsSince 41 problems in chapter 5 have been answered, more than 6826 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: First Course in Probability, edition: 8. This expansive textbook survival guide covers the following chapters and their solutions. First Course in Probability was written by and is associated to the ISBN: 9780136033134. Chapter 5 includes 41 full stepbystep solutions.

Adjusted R 2
A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

Analytic study
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

Arithmetic mean
The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average

Bernoulli trials
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

Biased estimator
Unbiased estimator.

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

Comparative experiment
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.

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

Conditional variance.
The variance of the conditional probability distribution of a 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.

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 twodimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

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.

Eficiency
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.

Enumerative study
A study in which a sample from a population is used to make inference to the population. See Analytic study

Error propagation
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.

Experiment
A series of tests in which changes are made to the system under study

Firstorder model
A model that contains only irstorder terms. For example, the irstorder response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irstorder model is also called a main effects model

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.

Generator
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.