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Probability And Statistics For Engineering And The Sciences 9th Edition Jay L. Devore - Solutions

Each customer making a particular Internet purchase must pay with one of three types of credit cards (think Visa, MasterCard, AmEx). Let Ai (i = 1, 2, 3) be the event that a type i credit card is used, with P(A1) = .5, P(A2) = .3, and P(A3) = .2. Suppose that the number of customers who make such a
a. Use the general formula for the variance of a linear combination to write an expression for V(aX + Y). Then let a = σY/σX, and show that ρ ≥ - 1. b. By considering V(aX - Y), conclude that r # 1. c. Use the fact that V(W) = 0 only if W is a constant to show that ρ = 1 only if Y = aX + b.
Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable-X for the right tire and Y for the left tire, with joint pdfa. What is the value of K? b. What is the probability that both tires are
Suppose a randomly chosen individual's verbal score X and quantitative score Y on a nationally administered aptitude examination have a joint pdfYou are asked to provide a prediction t of the individual's total score X + Y. The error of prediction is the mean squared error E[(X + Y - t)2]. What
a. Let X1 have a chi-squared distribution with parameter n1 (see Section 4.4), and let X2 be independent of X1 and have a chi-squared distribution with parameter v2. Use the technique of Example 5.22 to show that X1 + X2 has a chi-squared distribution with parameter v1 + v2. b. In Exercise 71 of
The accompanying data on flexural strength (MPa) for concrete beams of a certain type was introduced in Example 1.2.a. Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion, and state which estimator you used. b. Calculate
Using a long rod that has length m, you are going to lay out a square plot in which the length of each side is m. Thus the area of the plot will be σ2. However, you do not know the value of m, so you decide to make n independent measurements X1, X2,... , Xn of the length. Assume that each Xi has
Of n1 randomly selected male smokers, X1 smoked filter cigarettes, whereas of n2 randomly selected female smokers, X2 smoked filter cigarettes. Let p1 and p2 denote the probabilities that a randomly selected male and female, respectively, smoke filter cigarettes. a. Show that (X1/n1) 2 (X2/n2) is
Suppose a certain type of fertilizer has an expected Yield per acre of Âµ1 with variance Ïƒ2, whereas the expected Yield for a second type of fertilizer is Ïƒ2 with the same variance Ïƒ2. Let S21 and S22 denote the sample variances of Yields based on sample sizes n1 and n2, respectively, of
Consider a random sample X1, ... , Xn from the pdf f (x; θ) = .5(1 + θx) - 1 ≤ x ≤ 1 where - 1 ≤ u ≤ 1 (this distribution arises in particle physics). Show that θ^ = 3is an unbiased estimator of θ.
A sample of n captured Pandemonium jet fighters results in serial numbers x1, x2, x3, ... , Xn. The CIA knows that the air craft were numbered consecutively at the factory starting with a and ending with b, so that the total number of planes manufactured is β - α + 1 (e.g., if α = 17 and β =
Let X1, X2, ... , Xn represent a random sample from a Rayleigh distribution with pdfa. It can be shown that E(X2) = 2Î¸. Use this fact to construct an unbiased estimator of Î¸ based on Î£Xi2 (and use rules of expected value to show that it is unbiased). b.
Suppose the true average growth m of one type of plant during a 1year period is identical to that of a second type, but the variance of growth for the first type is σ2, whereas for the second type the variance is 4σ2. Let X1, ... , Xm be m independent growth observations on the first type [so
In Chapter 3, we defined a negative binomial rv as the number of failures that occur before the rth success in a sequence of independent and identical success/failure trials. The probability mass function (pmf) of X is nb(x; r, p) =a. Suppose that r ‰¥ 2. Show that p^ = (t - 1) / (X + r -
Let X1, X2, ... , Xn be a random sample from a pdf f (x) that is symmetric about m, so that , is an unbiased estimator of m. If n is large, it can be shown that V(), ≈ 1/(4n[ f (µ)]2). a. Compare V() to V() when the underling distribution is normal. b. When the underlying pdf is Cauchy (see
An investigator wishes to estimate the proportion of students at a certain university who have violated the honor code. Having obtained a random sample of n students, she realizes that asking each, "Have you violated the honor code?" will probably result in some untruthful responses. Consider the
The National Health and Nutrition Examination Survey (NHANES) collects demographic, socioeconomic, dietary, and health related information on an annual basis. Here is a sample of 20 observations on HDL cholesterol level (mg/dl) obtained from the 2009-2010 survey (HDL is "good" cholesterol; the
A diagnostic test for a certain disease is applied to n individuals known to not have the disease. Let X = the number among the n test results that are positive (indicating presence of the disease, so X is the number of false positives) and p = the probability that a disease free individual's test
Let X have a Weibull distribution with parameters a and b, so E(X) = β ∙ Γ(1 + 1/α) V(X) = β2Γ(1 + 2/α) - [Γ(1 + 1/α)]2} a. Based on a random sample X1,..., Xn, write equations for the method of moments estimators of β and α. Show that, once the estimate of α has been obtained, the
Let X denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of X iswhere - 1 a. Use the method of moments to obtain an estimator of Î¸, and then compute the estimate for this data. b. Obtain the maximum
Let X represent the error in making a measurement of a physical characteristic or property (e.g., the boiling point of a particular liquid). It is often reasonable to assume that E(X) = 0 and that X has a normal distribution. Thus the pdf of any particular measurement error is(where we have used
A vehicle with a particular defect in its emission control system is taken to a succession of randomly selected mechanics until r = 3 of them have correctly diagnosed the problem. Suppose that this requires diagnoses by 20 different mechanics (so there were 17 incorrect diagnoses). Let p =
The shear strength of each of ten test spot welds is determined, yielding the following data (psi): 392 376 401 367 389 362 409 415 358 375 a. Assuming that shear strength is normally distributed, estimate the true average shear strength and standard deviation of shear strength using the method of
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
Let X1, ... , Xn be a random sample from a gamma distribution with parameters a and b. a. Derive the equations whose solutions Yield the maximum likelihood estimators of a and b. Do you think they can be solved explicitly? b. Show that the mle of µ = αβ is µ^ = .
Let X1, X2,... , Xn represent a random sample from the Rayleigh distribution with density function given in Exercise 15. Determinea. The maximum likelihood estimator of u, and then calculate the estimate for the vibratory stress data given in that exercise. Is this estimator the same as the
Consider a random sample X1, X2,..., Xn from the shifted exponential pdfTaking u 5 0 gives the pdf of the exponential distribution considered previously (with positive density to the right of zero). An example of the shifted exponential distribution appeared in Example 4.5, in which the variable of
Consider the following sample of observations on coating thickness for low viscosity paint (“Achieving a Target Value for a Manufacturing Process: A Case Study,” J. of Quality Technology, 1992: 22–26):Assume that the distribution of coating thickness is normal (a normal probability plot
At time t = 0, 20 identical components are tested. The lifetime distribution of each is exponential with parameter λ. The experimenter then leaves the test facility unmonitored. On his return 24 hours later, the experimenter immediately terminates the test after noticing that y = 15 of the 20
An estimator θ^ is said to be consistent if for any e > 0, P(|θ^ - θ| ≥ e) ( ∞ as ( θ`. That is, θ^ is consistent if, as the sample size gets larger, it is less and less likely that θ^ will be further than e from the true value of θ. Show that is a consistent estimator of m when σ2 <
a. Let X1,... , Xn be a random sample from a uniform distribution on [0, Î¸]. Then the mle of u is Î¸^ = Y = max(Xi). Use the fact that Y ‰¤ y iff each Xi ‰¤ y to derive the cdf of Y. Then show that the pdf of Y = max(Xi) isb. Use the result of part
At time t = 0, there is one individual alive in a certain population. A pure birth process then unfolds as follows. The time until the first birth is exponentially distributed with parameter λ. After the first birth, there are two individuals alive. The time until the first gives birth again is
The mean squared error of an estimator θ^ is MSE (θ) - E(θ^ - θ^)2. If θ^ is unbiased, then MSE(θ^) = V(θ^), but in general MSE(θ^) = V(θ^) + (bias)2. Consider the estimator σ2 = Kσ2, where σ2 = sample variance. What value of K minimizes the mean squared error of this estimator when the
Let X1,... , Xn be a random sample from a pdf that is symmetric about m. An estimator for µ that has been found to perform well for a variety of underlying distributions is the Hodges-Lehmann estimator. To define it, first compute for each i ≤ j and each j = 1, 2, ... , n the pairwise average
When the population distribution is normal, the statistic median {| 1 -|, ... , Xn - , |}/.6745 can be used to estimate σ. This estimator is more resistant to the effects of outliers (observations far from the bulk of the data) than is the sample standard deviation. Compute both the
When the sample standard deviation S is based on a random sample from a normal population distribution, it can be shown that E(S) = √2/(n - 1)Γ(n/2)σ/Γ((n - 1)/2) Use this to obtain an unbiased estimator for s of the form cS. What is c when n = 20?
Each of n specimens is to be weighed twice on the same scale. Let Xi and Yi denote the two observed weights for the ith specimen. Suppose Xi and Yi are independent of one another, each normally distributed with mean value mi (the true weight of specimen i) and variance σ2. a. Show that the maXimum
The article from which the data in Exercise 1 was extracted also gave the accompanYing strength observations for cylinders:Prior to obtaining data, denote the beam strengths by X1,..., Xm and the cylinder strengths by Y1, . . . , Yn. Suppose that the Xi's constitute a random sample from a
As an example of a situation in which several different statistics could reasonably be used to calculate a point estimate, consider a population of N invoices. Associated with each invoice is its "book value," the recorded amount of that invoice. Let T denote the total book value, a known amount.
Urinary angiotensinogen (AGT) level is one quantitative indicator of kidney function. The article "Urinary Angiotensinogen as a Potential Biomarker of Chronic Kidney Diseases" (J. of the Amer. Society of Hypertension, 2008: 349-354) describes a study in which urinary AGT level (mg) was determined
In a random sample of 80 components of a certain type, 12 are found to be defective.a. Give a point estimate of the proportion of all such components that are not defective.b. A system is to be constructed by randomly selecting two of these components and connecting them in series, as shown
Each of 150 newly manufactured items is examined and the number of scratches per item is recorded (the items Let X = the number of scratches on a randomly chosen item, and assume that X has a Poisson distribution with parameter m. a. Find an unbiased estimator of m and compute the estimate for the
Consider a normal population distribution with the value of σ known. a. What is the confidence level for the interval ± 2.81 σ/√n? b. What is the confidence level for the interval ± 1.44 σ/√n? c. What value of za/2 in the CI formula (7.5) results in a confidence level of 99.7%? d.
A random sample of n 5 15 heat pumps of a certain type yielded the following observations on lifetime (in years): 2.0 1.3 6.0 1.9 5.1 .4 1.0 5.3 15.7 .7 4.8 .9 12.2 5.3 .6 a. Assume that the lifetime distribution is exponential and use an argument parallel to that of Example 7.5 to obtain a 95% CI
Consider the next 1000 95% CIs for µ that a statistical consultant will obtain for various clients. Suppose the data sets on which the intervals are based are selected independently of one another. How many of these 1000 intervals do you expect to capture the corresponding value of µ? What is the
The following observations are lifetimes (days) subsequent to diagnosis for individuals suffering from blood cancera. Can a confidence interval for true average lifetime be calculated without assuming anything about the nature of the lifetime distribution? Explain your reasoning. b. Calculate and
The article "Gas Cooking, Kitchen Ventilation, and Exposure to Combustion Products" (Indoor Air, 2006: 65-73) reported that for a sample of 50 kitchens with gas cooking appliances monitored during a one week period, the sample mean CO2 level (ppm) was 654.16, and the sample standard deviation was
The negative effects of ambient air pollution on children's lung function has been well established, but less research is available about the impact of indoor air pollution. The authors of "Indoor Air Pollution and Lung Function Growth Among Children in Four Chinese Cities" (Indoor Air, 2012: 3-11)
Determine the confidence level for each of the following large-sample one-sided confidence bounds: a. Upper bound: x̅ + .84s/√n b. Lower bound: x̅ - 2.05s/√n c. Upper bound: x̅ + .67s/√n
The alternating current (AC) breakdown voltage of an insulating liquid indicates its dielectric strength. The article "Testing Practices for the AC Breakdown Voltage Testing of Insulation Liquids" (IEEE Electrical Insulation Magazine, 1995: 21-26) gave the accompanying sample observations on
Exercise 1.13 gave a sample of ultimate tensile strength observations (ksi). Use the accompanying descriptive statistics output from Minitab to calculate a 99% lower confidence bound for true average ultimate tensile strength, and interpret the result.
The U.S. Army commissioned a study to assess how deeply a bullet penetrates ceramic body armor ("Testing Body Armor Materials for Use by the U.S. Army- Phase III," 2012). In the standard test, a cylindrical clay model is layered under the armor vest. A projectile is then fired, causing an
The article "Limited Yield Estimation for Visual Defect Sources" (IEEE Trans. on Semiconductor Manuf., 1997: 17-23) reported that, in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 201 of these passed the probe. Assuming a stable process,
Each of the following is a confidence interval for µ = true average (i.e., population mean) resonance frequency (Hz) for all tennis rackets of a certain type: (114.4, 115.6) (114.1, 115.9) a. What is the value of the sample mean resonance frequency? b. Both intervals were calculated from the same
TV advertising agencies face increasing challenges in reaching audience members because viewing TV programs via digital streaming is gaining in popularity. The Harris poll reported on November 13, 2012, that 53% of 2343 American adults surveyed said they have watched digitally streamed TV
In a sample of 1000 randomly selected consumers who had opportunities to send in a rebate claim form after purchasing a product, 250 of these people said they never did so ("Rebates: Get What You Deserve," Consumer Reports, May 2009: 7). Reasons cited for their behavior included too many steps in
The technology underlying hip replacements has changed as these operations have become more popular (over 250,000 in the United States in 2008). Starting in 2003, highly durable ceramic hips were marketed. Unfortunately, for too many patients the increased durability has been counterbalanced by an
The Pew Forum on Religion and Public Life reported on Dec. 9, 2009, that in a survey of 2003 American adults, 25% said they believed in astrology. a. Calculate and interpret a confidence interval at the 99% confidence level for the proportion of all adult Americans who believe in astrology. b.
A sample of 56 research cotton samples resulted in a sample average percentage elongation of 8.17 and a sample standard deviation of 1.42 ("An Apparent Relation Between the Spiral Angle f, the Percent Elongation E1, and the Dimensions of the Cotton Fiber," Textile Research J., 1978: 407-410).
A state legislator wishes to survey residents of her district to see what proportion of the electorate is aware of her position on using state funds to pay for abortions. a. What sample size is necessary if the 95% CI for p is to have a width of at most .10 irrespective of p? b. If the legislator
The superintendent of a large school district, having once had a course in probability and statistics, believes that the number of teachers absent on any given day has a Poisson distribution with parameter m. Use the accompanying data on absences for 50 days to obtain a large sample CI for µ.
Reconsider the CI (7.10) for p, and focus on a confidence level of 95%. Show that the confidence limits agree quite well with those of the traditional interval (7.11) once two successes and two failures have been appended to the sample.
Determine the values of the following quantities: a. t.1,15 b. t.05,15 c. t.05,25 d. t.05,40 e. t.005,40
Determine the t critical value(s) that will capture the desired t-curve area in each of the following cases: a. Central area = .95, df = 10 b. Central area = .95, df = 20 c. Central area = .99, df = 20 d. Central area = .99, df = 50 e. Upper-tail area = .01, df = 25 f. Lower-tail area = .025, df = 5
Suppose that a random sample of 50 bottles of a particular brand of cough syrup is selected and the alcohol content of each bottle is determined. Let µ denote the average alcohol content for the population of all bottles of the brand under study. Suppose that the resulting 95% confidence interval
Determine the t critical value for a two-sided confidence interval in each of the following situations: a. Confidence level = 95%, df = 10 b. Confidence level = 95%, df = 15 c. Confidence level = 99%, df = 15 d. Confidence level = 99%, n = 5 e. Confidence level = 98%, df = 24 f. Confidence level =
Determine the t critical value for a lower or an upper confidence bound for each of the situations described in Exercise 30. a. Confidence level = 95%, df = 10 b. Confidence level = 95%, df = 15 c. Confidence level = 99%, df = 15 d. Confidence level = 99%, n = 5 e. Confidence level = 98%, df =
According to the article "Fatigue Testing of Condoms" (Polymer Testing, 2009: 567-571), "tests currently used for condoms are surrogates for the challenges they face in use," including a test for holes, an inflation test, a package seal test, and tests of dimensions and lubricant quality (all
The article "Measuring and Understanding the Aging of Kraft Insulating Paper in Power Transformers" (IEEE Electrical Insul. Mag., 1996: 28-34) contained the following observations on degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle
A sample of 14 joint specimens of a particular type gave a sample mean proportional limit stress of 8.48 MPa and a sample standard deviation of .79 MPa ("Characterization of Bearing Strength Factors in Pegged Timber Connections," J. of Structural Engr., 1997: 326-332). a. Calculate and interpret a
Silicone implant augmentation rhinoplasty is used to correct congenital nose deformities. The success of the procedure depends on various biomechanical properties of the human nasal periosteum and fascia. The article "Biomechanics in Augmentation Rhinoplasty" (J. of Med. Engr. and Tech., 2005:
A normal probability plot of the n = 26 observations on escape time given in Exercise 36 of Chapter 1 shows a substantial linear pattern; the sample mean and sample standard deviation are 370.69 and 24.36, respectively. a. Calculate an upper confidence bound for population mean escape time using a
A study of the ability of individuals to walk in a straight line ("Can We Really Walk Straight?" Amer. J. of Physical Anthro., 1992: 19-27) reported the accompanying data on cadence (strides per second) for a sample of n 5 20 randomly selected healthy men.A normal probability plot gives substantial
Ultra high performance concrete (UHPC) is a relatively new construction material that is characterized by strong adhesive properties with other materials. The article "Adhesive Power of Ultra High Performance Concrete from a Thermodynamic Point of View" (J. of Materials in Civil Engr., 2012:
Exercise 72 of Chapter 1 gave the following observations on a receptor binding measure (adjusted distribution volume) for a sample of 13 healthy individuals: 23, 39, 40, 41, 43, 47, 51, 58, 63, 66, 67, 69, 72. a. Is it plausible that the population distribution from which this sample was selected
A CI is desired for the true average stray-load loss µ (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with σ = 3.0. a. Compute a 95% CI for m when µ = 25 and = 58.3. b. Compute
Exercise 13 of Chapter 1 presented a sample of n = 153 observations on ultimate tensile strength, and Exercise 17 of the previous section gave summary quantities and requested a large-sample confidence interval. Because the sample size is large, no assumptions about the population distribution are
A more extensive tabulation of t critical values than what appears in this book shows that for the t distribution with 20 df, the areas to the right of the values .687, .860, and 1.064 are .25, .20, and .15, respectively. What is the confidence level for each of the following three confidence
Determine the values of the following quantities: a. x2.1,15 b. x2.1,25 c. x2.01,25 d. x2.005,25 e. x2.99,25 f. x2.995,25
Determine the following: a. The 95th percentile of the chi-squared distribution with v = 10 b. The 5th percentile of the chi-squared distribution with v = 10 c. P(10.98 ≤ x2 ≤ 36.78), where x2 is a chi-squared rv with v = 22 d. P(x2, 14.611 or x2. 37.652), where x2 is a chisquared rv with v = 25
The amount of lateral expansion (mils) was determined for a sample of n = 9 pulsed-power gas metal arc welds used in LNG ship containment tanks. The resulting sample standard deviation was s = 2.81 mils. Assuming normality, derive a 95% CI for σ2 and for σ.
Wire electrical-discharge machining (WEDM) is a process used to manufacture conductive hard metal components. It uses a continuously moving wire that serves as an electrode. Coating on the wire electrode allows for cooling of the wire electrode core and provides an improved cutting performance. The
The article "Concrete Pressure on Formwork" (Mag. of Concrete Res., 2009: 407-417) gave the following observations on maximum concrete pressure (kN/m2):a. Is it plausible that this sample was selected from a normal population distribution? b. Calculate an upper confidence bound with confidence
Example 1.11 introduced the accompanying observations on bond strength.a. Estimate true average bond strength in a way that conveys information about precision and reliability. b. Calculate a 95% CI for the proportion of all such bonds whose strength values would exceed 10.
The article "Distributions of Compressive Strength Obtained from Various Diameter Cores" (ACI Materials J., 2012: 597-606) described a study in which compressive strengths were determined for concrete specimens of various types, core diameters, and length to-diameter ratios. For one particular
For those of you who don't already know, dragon boat racing is a competitive water sport that involves 20 paddlers propelling a boat across various race distances. It has become increasingly popular over the last few years. The article "Physiological and Physical Characteristics of Elite Dragon
Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation .75. a. Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 20 specimens from the seam was 4.85. b. Compute a
A journal article reports that a sample of size 5 was used as a basis for calculating a 95% CI for the true average natural frequency (Hz) of delaminated beams of a certain type. The resulting interval was (229.764, 233.504). You decide that a confidence level of 99% is more appropriate than the
Unexplained respiratory symptoms reported by athletes are often incorrectly considered secondary to exercise-induced asthma. The article "High Prevalence of Exercise-Induced Laryngeal Obstruction in Athletes" (Medicine and Science in Sports and Exercise, 2013: 2030-2035) suggested that many such
High concentration of the toxic element arsenic is all too common in groundwater. The article "Evaluation of Treatment Systems for the Removal of Arsenic from Groundwater" (Practice Periodical of Hazardous, Toxic, and Radioactive Waste Mgmt., 2005: 152-157) reported that for a sample of n = 5 water
Aphid infestation of fruit trees can be controlled either by spraying with pesticide or by inundation with ladybugs. In a particular area, four different groves of fruit trees are selected for experimentation. The first three groves are sprayed with pesticides 1, 2, and 3, respectively, and the
It is important that face masks used by firefighters be able to withstand high temperatures because firefighters commonly work in temperatures of 200-500°F. In a test of one type of mask, 11 of 55 masks had lenses pop out at 250°. Construct a 90% upper confidence bound for the true proportion of
The accompanying data on crack initiation depth (mm) was read from a lognormal probability plot that appeared in the article "Incorporating Small Fatigue Crack Growth in Probabilistic Life Prediction: Effect of Stress Ratio in Ti-6Al-2Sn-6Mo" (Intl. J. of Fatigue, 2013: 83-95). Although the pattern
In Example 6.8, we introduced the concept of a censored experiment in which n components are put on test and the experiment terminates as soon as r of the components have failed. Suppose component lifetimes are independent, each having an exponential distribution with parameter l. Let Y1 denote the
Let X1, X2,..., Xn be a random sample from a continuous probability distribution having median m, (so that P(Xi ‰¤ µÌƒ) = P(Xi ‰¥ µÌƒ) = .5).a. Show thatSo that (min(xi), max(xi)) is a 100(1 - Î±)% confidence interval for
Let X1, X2,..., Xn be a random sample from a uniform distribution on the interval [0, Ã¸], so thatThen if Y = max (Xi), it can be shown that the rv U = Y/Ã¸ has density function a. Use fU(u) to verify that and use this to derive a 100(1 - Î±)% CI for
On the basis of extensive tests, the yield point of a particular type of mild steel-reinforcing bar is known to be normally distributed with σ = 100. The composition of bars has been slightly modified, but the modification is not believed to have affected either the normality or the value of s. a.
Let 0 ‰¤ Î³ ‰¤ a. Then a 100(1 - Î±)% CI for m when n is large isThe choice Î³ = Î±/2 yields the usual interval derived in Section 7.2; if Î³ ‰ Î±/2, this interval is not symmetric about
Suppose x1, x2,..., xn are observed values resulting from a random sample from a symmetric but possibly heavy-tailed distribution. Let xÌƒ, and fs denote the sample median and fourth spread, respectively. Chapter 11 of Understanding Robust and Exploratory Data Analysis (see the
a. Use the results of Example 7.5 to obtain a 95% lower confidence bound for the parameter l of an exponential distribution, and calculate the bound based on the data given in the example. b. If lifetime X has an exponential distribution, the probability that lifetime exceeds t is P(X > t) = e-γt.

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