Consider randomly selecting n segments of pipe and determining the corrosion loss (mm) in the wall thickness for each one. Denote these corrosion losses by Y1,..., Yn. The article “A Probabilistic Model for a Gas Explosion Due to Leakages in the Grey Cast Iron Gas Mains” (Reliability Engr. and System Safety (2013:270-279) proposes a linear corrosion model: Yi = tiR, where ti is the age of the pipe and R, the corrosion rate, is exponentially distributed with parameter λ. Obtain the maximum likelihood estimator of the exponential parameter (the resulting mle appears in the cited article). [Hint: If c > 0 and X has an exponential distribution, so does cX.]
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Chapter 6 Solutions
Probability and Statistics for Engineering and the Sciences
- Consider randomly selecting n segments of pipe and determining the corrosion loss (mm) in the wall thickness for each one. Denote these corrosion losses by Y₁' Yn. The article "A Probabilistic Model for a Gas Explosion Due to Leakages in the Grey Cast Iron Gas Mains"+ proposes a linear corrosion model: Y; = t;R, where t; is the age of the pipe and R, the corrosion rate, is exponentially distributed with parameter 1. Obtain the maximum likelihood estimator of the exponential parameter (the resulting mle appears in the cited article). [Hint: If c> 0 and X has an exponential distribution, so does cX.] O Â = O Â = O λ = * * O n Srit) i = 1 n j = 1 Σ i = 1 n n i = 1 n LY i = 1 n 0 1 = L (rt) 2 i = 1 | = 1 n n Y; | = 1arrow_forwardThe spotted lanternfly, Lycorma delicatula, is an invasive species to the United States that has the potential to do significant agricultural damage. An ecologist is studying the relationship between the size of the female spotted lanternflies and the number of eggs they produce. The data are summarized below. Length of insect: AVG = 1 inch, SD = 0.15 inchNumber of eggs: AVG = 40 eggs, SD = 5 eggsr = 0.2 Using regression, we can say that the average number of eggs produced by female spotted lanternflies who are 1.1 inch long is closest to... Group of answer choices 42 39 40 41arrow_forwardSuppose that the weight of a type of organism is governed by a power law relationship with its length from snout to tail and the thickness of its central vertebrae W = cLpVq. One specimen weighed 37 kg with a length of 1.6 m and vertebral thickness 1 cm. A second specimen weighed 45 kg with a length of 1.6 m and vertebral thickness 1.3 cm. A third specimen weighed 56 kg with a length of 3.1 m and vertebral thickness 1.2 cm. Write an equation with the correct coefficient and parameters values.arrow_forward
- Given: A regression of ln(wage) on educ, exper, exper2, female, married, numdep and two interaction terms female ∗ edu and female ∗ married. (For the interaction terms I multiplied female data x edu data and so forth) Question: What does the coefficient on the interaction term measure? Interpret the coefficients on the interaction term, female ∗ edu and female ∗ married.arrow_forwardA sociologist wants to determine if the life expectancy of people in Africa is less than the life expectancy of people in Asia. The data obtained is shown in the table below. Africa Asia = 63.3 yr. 1 X,=65.2 yr. 2 o, = 9.1 yr. = 7.3 yr. n1 = 120 = 150arrow_forwardAn experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsións have been added during mixing) to that of unmodified mortar resulted in x = 18.11 kgf/cm2 for the modified mortar (m = 42) and y = 16.88 kgf/cm2 for the unmodified mortar (n = 31). Let ₁ and ₂ be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (a) Assuming that o₁ = 1.6 and ₂ = 1.3, test Ho: ₁ - ₂ = 0 versus H₂: H₁ - H₂> 0 at level 0.01. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) Z = P-value = State the conclusion in the problem context. O Fail to reject Ho. The data suggests that the difference in average tension bond strengths exceeds 0. Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths…arrow_forward
- Q3) An experiment was carried out to investigate variation of solubility of chemical X in water. The quantities in kg that dissolved in 1 liter at various temperatures are show in the table (1). Table (1) Temperature C Mass of X 2.1 2.6 2.9 3.3 15 20 25 30 35 4 50 5.1 70 7 Use the proper methods to answer the following questions: a) Draw a scatter diagram to show the data. b) Estimate the temperature based on the mass of X. c) What quantity might be expected to dissolve at 42 C? Find the quantity that your cquation indicates would dissolve at 10 C and comment on your answer.arrow_forwardArm circumferences (cm) and heights (cm) are measured from randomly selected adult females. The 139 pairs of measurements yield x = 31.99 cm, y = 163.33 cm, r= 0.032, P-value = 0.708, and y = 158 + 0.1703x. Find the best predicted value of y (height) given an adult female with an arm circumference of 35.0 cm. Let the predictor variable x be arm circumference and the response variable y be height. Use a 0.05 significance level. %3D ..... The best predicted value is cm. (Round to two decimal places as needed.)arrow_forwardThe depth of wetting of a soil is the depth to which water content will increase owing to extemal factors. The article "Discussion of Method for Evaluation of Depth of Wetting in Residential Areas" (J. Nelson, K. Chao, and D. Overton, Journal of Geotechnical and Geoenvironmental Engineering, 2011:293-296) discusses the relationship between depth of wetting beneath a structure and the age of the structure. The article presents measurements of depth of wetting, in meters, and the ages, in years, of 21 houses, as shown in the following table. Age Depth 7.6 4 4.6 6.1 9.1 3 4.3 7.3 5.2 10.4 15.5 5.8 10.7 4 5.5 6.1 10.7 10.4 4.6 7.0 6.1 14 16.8 10 9.1 8.8 Compute the least-squares line for predicting depth of wetting (y) from age (x). b. Identify a point with an unusually large x-value. Compute the least-squares line that results from deletion of this point. Identify another point which can be classified as an outlier. Compute the least-squares line that results from deletion of the outlier,…arrow_forward
- Alcohol use in the United States increased during the first year of the COVID pandemic, as did the number of alcohol-induced deaths (such as alcoholic liver disease, accidental alcohol poisoning, disorders due to acute intoxication). Here is a figure from the CDC representing the "Rates of alcohol-induced deaths in the United States in 2020, broken down by sex and age group." Figure 2. Rates of alcohol-induced deaths, by sex and age group: United States, 2020 Age group (years) Under 25 0.1 25-34 35-44 45-54 55-64 65-74 75-84 85 and over Under 25 25-34 35-44 45-54 55-64 65-74 75-84 85 and over 0 0.3 3.9 2.9 6.4 10.2 7.9 10 12.9 12.8 16.7 20 21.0 21.8 24.5 Female Male 38.5 SOURCE: National Center for Health Statistics, National Vital Statistics System, Mortality. I 40 43.4 30 Deaths per 100,000 population 50 59.0 I 60 70 Interpret the bottom-most bar (gray bar with the value "12.8" written next to it) as a sentence in context. Enter your answer here Select ALL correct interpretations of…arrow_forwardCell Phone Radiation Listed below are the measured radiation absorption rates (in W/kg) corresponding to these cell phones: iPhone 5S, BlackBerry Z30, Sanyo Vero, Optimus V, Droid Razr, Nokia N97, Samsung Vibrant, Sony Z750a, Kyocera Kona, LG G2, and Virgin Mobile Supreme. The data are from the Federal Communications Commission (FCC). The media often report about the dangers of cell phone radiation as a cause of cancer. The FCC has a standard that a cell phone absorption rate must be 1.6 W/kg or less. If you are planning to purchase a cell phone, are any of the measures of center the most important statistic? Is there another statistic that is most relevant? If so, which one?arrow_forwarda) We conduct a regression of size on hhinc, owner, hhsize, hhsize2,and hhsize3. We do not include the constant. The regression output is reported in Table 3. Would you conclude that the home size increases with the household size? Interpret the sign and magnitude of the estimated coefficients of hhsize1, hhsize2, and hhsize3.arrow_forward
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