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applied statistics and probability for engineers

Questions and Answers of Applied Statistics And Probability For Engineers

=+this with the corresponding maximum transferable load (kN) as measured in the laboratory.The data is given here:Calc: Meas: Calc: Meas:14.2 13.7 14.3 13.4 16.0 13.7 21.4 21.4 16.5 15.4 17.6 14.8
=+the article “Interfacial Bond Strength Characteristics of FRP and RC Substrate” (J. of Compos.Constr., 2012: 35–43), investigators developed a method to mathematically model bond strength
=+12. Historically, reinforced concrete structures used externally bonded steel plates to add strength and support. Recently, fiber reinforced polymer(FRP) plates have been used instead of steel
=+ Based on this, compute the sample correlation coefficient and interpret its value. How would you characterize this correlation—as strong, moderate, or weak?
=+296–299) reported on an investigation in which lead hip internal peak rotational velocity (x) and trailing hip peak external rotational velocity (y)were determined for a sample of 15 golfers.
=+11. Torsion during external rotation and extension of the hip may explain why acetabular labral tears occur in professional athletes. The article“Hip Rotational Velocities During the Full Golf
=+c. Calculate the value of the sample correlation coefficient. Does it confirm your impression from the scatterplot?
=+b. Construct a scatterplot of the data. What does it suggest about the general nature of the relationship between Cl and Co?
=+a. Construct boxplots of both the clockwise and counterclockwise direction observations, and comment on any interesting features.
=+Subj: 1 2 3 4 5 6 7 Cl: 57.9 35.7 54.5 56.8 51.1 70.8 77.3 Co: 44.2 52.1 60.2 52.7 47.2 65.6 71.4 Subj: 8 9 10 11 12 13 14 Cl: 51.6 54.7 63.6 59.2 59.2 55.8 38.5 Co: 48.8 53.1 66.3 59.8 47.5 64.5
=+angles of the head in the clockwise anterior, posterior, right, and left directions for 14 randomly selected subjects. Consider the accompanying data on average anterior maximum inclination angle
=+10. Head movement evaluations are important because individuals, especially those who are disabled, may be able to operate communications aids in this manner. The article “Constancy of Head
=+f. Distance from a Stanford University student’s home town to campus and grade point average
=+e. Fuel efficiency and 3-year operating cost
=+d. Vehicle speed (mph, from 20 to 100) and fuel efficiency (mpg)
=+c. Incomes of husbands and wives when both have full-time jobs
=+a. Maximum daily temperature and cooling cost
=+9. For each of the following pairs of variables, indicate whether you would expect a positive correlation, a negative correlation, or little or no correlation.Explain your choice.
=+ Construct a scatterplot of the data. How would you describe the nature of the relationship between the two variables? Does it seem to be the case that COI and API are closely related?
=+ Consider the following monthly API and statewide crude oil index (COI) values for California during 2010−11, obtained from the California Department of Transportation.COI API COI API 385.1
=+factors. From about the mid-1990s to 2010, Kentucky’s annual average API and DPI were found to be closely related to the annual average crude oil price. Based on this, the authors suggested that
=+8. Researchers considered how the construction cost of highway resurfacing projects in Kentucky were affected by that state’s asphalt price index(API) and diesel price index (DPI) among other
=+ Construct a scatterplot of the data. How would you describe the nature of the relationship between the two variables?
=+researchers propose a generalized water yield model for watersheds. One important watershedspecific component of the model is , a coefficient characterizing the watershed’s annual water yield
=+7. In surface water hydrology, a common problem is the estimation of long-term annual yield from ungauged watersheds. In the article “Generalized Mediterranean Annual Water Yield
=+ Construct a scatterplot of the data. How would you describe the nature of the relationship between the two variables?
=+6. Calcium phosphate cement is gaining increasing attention for use in bone repair applications. The article “Short-Fibre Reinforcement of Calcium Phosphate Bone Cement” (J. of Engr. in Med.,
=+c. What do the plots of parts (a) and (b) suggest about the nature of the relationship between the two variables?
=+b. Construct a scatterplot in which the axes intersect at (55, 100), as was done in the cited article. Does this plot seem preferable to the one in part (a)? Explain your reasoning.
=+a. Construct a scatterplot in which the axes intersect at (0, 0). Mark 0, 20, 40, 60, 80, and 100 on the horizontal axis and 0, 50, 100, 150, 200, and 250 on the vertical axis.
=+cheese, not the poor cousin widely available in the United States.x: 59 63 68 72 74 78 83 y: 118 182 247 208 197 135 132
=+5. The article “Objective Measurement of the Stretch-ability of Mozzarella Cheese” (J. of Texture Studies, 1992: 185–194) reported on an experiment to investigate how the behavior of
=+c. Construct a scatterplot of the data. Does it appear that recovered oil could be accurately predicted by the value of added oil? Explain your reasoning.
=+b. Do the values of the recovered oil appear to be perfectly linearly related to the added oil values?Why or why not?
=+a. For each observation, determine the percentage of oil recovery by wheat straw. Is this percentage relatively constant across all observations? Was the percentage higher at certain added oil
=+Its Effect on Biodegradation” (J. Hazard. Toxic Radioact. Waste, 2012: 75–78), researchers examined how wheat straw could be used to extract crude oil from a water surface. An experiment was
=+4. Open water oil spills, such as the Deepwater Horizon spill of 2010, can wreak terrible consequences on the environment and be expensive to clean up. Many physical and biological methods have
=+3. In the article referenced in Exercise 2, the relationship between the number of beds in a barrack and the cost of the building was also investigated.Number of Beds Cost 22 418,930 40 609,386 40
=+c. Construct a scatterplot of the data. Does it appear that cost could be accurately predicted by the value of floor area? Explain your reasoning.
=+b. Do the values of cost appear to be perfectly linearly related to the floor area values?
=+a. Construct stem-and-leaf displays of both floor area and cost. Comment on any interesting features.
=+2. The article “Case Adaptation Method of Case-Based Reasoning for Construction Cost Estimation in Korea” (J. Constr. Engr. Mgmt., 2012: 43–52) provided data on military barrack projects
=+Solar Absorptance: .81 .78 .69 .65 .48 Create a scatterplot for this data. How would you characterize the relationship between these two variables? Is the desired inverse relationship between
=+1. In the article “Analysis of the Thermal Properties of Air-Conditioning-Type Building Materials” (Solar Energy, 2012: 2967–2974), researchers investigated thermal properties of building
Consider the non-component-wise transformation\[y_{i} \mapsto \frac{y_{i}^{\lambda}}{\lambda \dot{y}^{\lambda-1}}\]where \(\dot{y}\) is the geometric mean of the components of \(y \in
For the setting of the previous exercise, show that \(Y\) is distributed according to the mixture with density\[m(y)=(1-ho) \phi(y)+ho \psi(y)+o(ho)=\phi(y)(1-ho+ho \zeta(y))+o(ho)\]where
In the setting of the previous exercise, let \(W=L \varepsilon\), where \(L\) is a Boolean matrix. Show that \(W\) is a process defined on general planar regions and that it coincides with the
Use the Gaussian model with second moments given in the previous exercise to compute a pseudo-log likelihood l0(β,σ)l0(β,σ) for the parameter (β,σ)(β,σ). Show that the pseudo log-likelihood
McCullagh and Nelder (1989, Sect. 14.5) describe an experiment by S. Arnold and P. Verrell on the interbreeding of southern Appalachian mountain dusky salamanders. Each male has six breeding
Use the table () function to extract the distinct values for vowel diversity, consonant diversity, tone diversity and total phoneme diversity. What does this tell you?
Consider the following statement taken from Sect. 5.5. Any credible analysis that accommodates the virtual randomization must be invariant with respect to the same group, and similar remarks apply to
Procedural invariance. Consider a sample of 512 observations generated according to the model in the previous exercise. The estimation procedure is invariant if
For the model with persistent aviary patterns described at the end of Sect. 5.4.2, compute and plot the REML profile \(\log\) likelihood for \(\tau\) in the range \(0.5 \leq \tau \leq 24\). Use PC1
114. Show that if A1, A2, and A3 are independent events, then P(A1⏐ A2 A3) P(A1)
113. A box contains the following four slips of paper, each having exactly the same dimensions: (1) win prize 1; (2) win prize 2; (3) win prize 3; (4) win prizes 1, 2, and 3. One slip will be
112. Consider four independent events A1, A2, A3, and A4 and let pi P(Ai) for i 1, 2, 3, 4. Express the probability that at least one of these four events occurs in terms of the pis, and do the
111. A personnel manager is to interview four candidates for a job. These are ranked 1, 2, 3, and 4 in order of preference and will be interviewed in random order. However, at the conclusion of each
110. A particular airline has 10 A.M. flights from Chicago to New York, Atlanta, and Los Angeles. Let A denote the event that the New York flight is full and define events B and C analogously for the
109. Four engineers, A, B, C, and D, have been scheduled for job interviews at 10 A.M. on Friday, January 13, at Random Sampling, Inc. The personnel manager has scheduled the four for interview rooms
108. In a Little League baseball game, team A’s pitcher throws a strike 50% of the time and a ball 50% of the time, successive pitches are independent of one another, and the pitcher never hits a
107. A subject is allowed a sequence of glimpses to detect a target. Let Gi {the target is detected on the ith glimpse}, with pi P(Gi). Suppose the Gis are independent events and write an
106. One method used to distinguish between granitic (G) and basaltic (B) rocks is to examine a portion of the infrared spectrum of the sun’s energy reflected from the rock surface.Let R1, R2, and
105. Disregarding the possibility of a February 29 birthday, suppose a randomly selected individual is equally likely to have been born on any one of the other 365 days.a. If ten people are randomly
104. A company uses three different assembly lines—A1, A2, and A3—to manufacture a particular component. Of those manufactured by line A1, 5% need rework to remedy a defect, whereas 8% of A2’s
103. Refer to Exercise 102. Suppose that 50% of the overnight parcels are sent via express mail service E2 and the remaining 10% are sent via E3. Of those sent via E2, only 1% arrive late, whereas 5%
102. A certain company sends 40% of its overnight mail parcels via express mail service E1. Of these parcels, 2% arrive after the guaranteed delivery time (denote the event “late delivery” by L).
101. A system consists of two components. The probability that the second component functions in a satisfactory manner during its design life is .9, the probability that at least one of the two
100. One percent of all individuals in a certain population are carriers of a particular disease. A diagnostic test for this disease has a 90% detection rate for carriers and a 5%detection rate for
b. Given that a fastener passed inspection, what is the probability that it passed the initial inspection and did not need recrimping?
a. What is the probability that a randomly selected incoming fastener will pass inspection either initially or after recrimping?
99. Fasteners used in aircraft manufacturing are slightly crimped so that they lock enough to avoid loosening during vibration. Suppose that 95% of all fasteners pass an initial inspection. Of the 5%
98. Each contestant on a quiz show is asked to specify one of six possible categories from which questions will be asked.Suppose P(contestant requests category i) 1 6 and successive contestants
97. A chemical engineer is interested in determining whether a certain trace impurity is present in a product. An experiment has a probability of .80 of detecting the impurity if it is present. The
95. Individual A has a circle of five close friends (B, C, D, E, and F). A has heard a certain rumor from outside the circle and has invited the five friends to a party to circulate the rumor. To
94. A transmitter is sending a message by using a binary code, namely, a sequence of 0’s and 1’s. Each transmitted bit (0 or 1) must pass through three relays to reach the receiver. At each
93. One satellite is scheduled to be launched from Cape Canaveral in Florida, and another launching is scheduled for Vandenberg Air Force Base in California. Let A denote the event that the
92. An employee of the records office at a certain university currently has ten forms on his desk awaiting processing. Six of these are withdrawal petitions and the other four are course substitution
c. Given that the selected can had a surface defect, what is the probability that it came from line 1?
b. If the selected can came from line 1, what is the probability that it had a blemish?
a. What is the probability that the can was produced by line 1? That the reason for nonconformance is a crack?
91. A factory uses three production lines to manufacture cans of a certain type. The accompanying table gives percentages of nonconforming cans, categorized by type of nonconformance, for each of the
90. A small manufacturing company will start operating a night shift. There are 20 machinists employed by the company.a. If a night crew consists of 3 machinists, how many different crews are
89. Suppose identical tags are placed on both the left ear and the right ear of a fox. The fox is then let loose for a period of time. Consider the two events C1 {left ear tag is lost} and C2
88. Professor Stan der Deviation can take one of two routes on his way home from work. On the first route, there are four railroad crossings. The probability that he will be stopped by
87. Refer to the assumptions stated in Exercise 80 and answer the question posed there for the system in the accompanying picture. How would the probability change if this were a subsystem connected
86.a. A lumber company has just taken delivery on a lot of 10,000 2 4 boards. Suppose that 20% of these boards(2,000) are actually too green to be used in first-quality construction. Two boards are
85. A quality control inspector is inspecting newly produced items for faults. The inspector searches an item for faults in a series of independent fixations, each of a fixed duration.Given that a
84. Seventy percent of all vehicles examined at a certain emissions inspection station pass the inspection. Assuming that successive vehicles pass or fail independently of one another, calculate the
83. Components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). The first inspector detects 90% of all defectives that are
82. Consider independently rolling two fair dice, one red and the other green. Let A be the event that the red die shows 3 dots, B be the event that the green die shows 4 dots, and C be the event
81. Refer back to the series-parallel system configuration introduced in Example 2.35, and suppose that there are only two cells rather than three in each parallel subsystem [in Figure 2.14(a),
80. Consider the system of components connected as in the accompanying picture. Components 1 and 2 are connected in parallel, so that subsystem works iff either 1 or 2 works;
79. Two pumps connected in parallel fail independently of one another on any given day. The probability that only the older pump will fail is .10, and the probability that only the newer pump will
78. A boiler has five identical relief valves. The probability that any particular valve will open on demand is .95. Assuming independent operation of the valves, calculate P(at least one valve
77. An aircraft seam requires 25 rivets. The seam will have to be reworked if any of these rivets is defective. Suppose rivets are defective independently of one another, each with the same
76. The probability that a grader will make a marking error on any particular question of a multiple-choice exam is .1. If there are ten questions and questions are marked independently, what is the
75. One of the assumptions underlying the theory of control charting (see Chapter 16) is that successive plotted points are independent of one another. Each plotted point can signal either that a
74. Suppose that the proportions of blood phenotypes in a particular population are as follows:A B AB O.42 .10 .04 .44 Assuming that the phenotypes of two randomly selected individuals are
73. If A and B are independent events, show that A and B are also independent. [Hint: First establish a relationship between P(A B), P(B), and P(A B).]
72. In Exercise 13, is any Ai independent of any other Aj?Answer using the multiplication property for independent events.

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