DQE+-+Homework+Solutions+Index

DQE - Homework Solutions Index (DQE Prep) (GWU EMSE-271) ( And lectures being added )
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b. What is the probability of selecting a defective on the first three draws? c. What is the probability of selecting a defective on the first or second draws? d. What is the probability that a defect was drawn on the first draw given two defects were drawn by the third draw? ||  ||   ||
 * **Source** ||  ||   ||   || **Problems** ||   ||   ||
 * Lecture 1 ||  || S17 ||   || The probability of drawing an ace of spades in a deck of 52 cards equals 1/52. However, if I tell you that I have an ace in my hands, the probability of it being the ace of spades equals ||   ||   ||
 * ||  || S20 -22 ||   || Example 4: Given a batch of 100 items, 10 being defectivesa. What is the probability of selecting a non defective item?
 * ||  || S27 ||   || Example 6:When a student attempts to log on to a computer time-sharing system, either all ports are busy (J )ß in which case the student will fail to obtain access, or else there is at least one port free (W ), in which case the student will be successful in accessing the system. ||   ||   ||
 * ||  || S28 ||   || Example 7: Consider the experiment in which batteries are examined until a good (S)is obtained. ||   ||   ||
 * ||  || S29 ||   || Example 5: Let the probability of an item being defective, p, be .01, .05 or .10 with probability .6, .3, .1 respectively. If two samples are selected and tested what is the probability that p is .01, .05, and .10 given 0, 1, or 2 defects are found. ||   ||   ||
 * Lecture 2 ||  || S51 ||   || A machine that produces ball bearings has initially been set so that the true average diameter of the bearings is .500 in. A bearing is acceptable if the diameter is within .004in of this target value. Suppose, however, that the setting has changes during the course of production, so that bearings have normally distributed diameters with mean value .499 and standard deviation .002in. What percentage of bearings will not be acceptable? ||   ||   ||
 * ||  || S53 ||   || Suppose only 40% of all drivers in a certain state regularly wear a seatbelt. A random sample of 500 drivers is selected. What is the probability that between 180 and 230 drivers regularly wear there seatbelts? ||   ||   ||
 * ||  || S56 ||   || Suppose customers arrive at a bank independently from one another with an interarrival time that is exponentially distributed and mean interarrival time of 15 minutes. The bank operates for 8 hours. What is the probability that the 48th customers arrives before the bank closes? ||   ||   ||
 * ||  || S61 ||   || Example 15 (Continued): The following sample consists of n = 20 observations on dielectric breakdown voltage of a piece of epoxy resin appeared in the article "Maximum Likelihood Estimation in the 3-parameter Weibull distribution" (IEEE Trans. on Dielectrics and Elec. Insul. 1996: 43-55). ||   ||   ||
 * Homework Set 2 ||  || 1 ||   || Airlines sometimes overbook flights. Suppose that for a plane with 50 seats, 55 passengers have tickets. Define the random variable Y as the number of ticketed passengers who actually show up for the flight. The probability mass function of Y appears in the accompanying table. ||   ||   ||
 * ||  || 2 ||   || An appliance dealer sells three different models of upright freezers having 13.5, 15.9 and 19.1 cubic feet storage space, respectively. Let X the amount of storage space purchased by the next customer to buy a freezer. Suppose that X has pmf. ||   ||   ||
 * ||  || 3 ||   || A //k-out-of-n// system is one that will function if and only if at least k out of n individual components in the system function. If individual components functions independently from one another, each with probability .9, what is the probability that 3-out-of 5 system functions. ||   ||   ||
 * ||  || 4 ||   || Shafts question X~Binomial ||   ||   ||
 * Lecture 3 ||  || S69 - 95 ||   || Dielectric breakdown voltage data (n=20) {Computing Confidence Interval; connection Hypothesis Testing, Type I and Type II Errors, definiton of the p-value, Goodness of Fit (MOM/MLE) ||   ||
 * Lecture 4 ||  || M ||   || More example 15, Credibility Intervals. Probabaiality Plots. ||   ||   ||   ||
 * Homework Set 3a ||  || 1 ||   || 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 is (7.8, 9.4) ||   ||   ||
 * ||  || 2 ||   || Suppose that 10% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be reworked. What is the (approximately) probability that X is ||   ||   ||
 * ||  || 3 ||   || A random sample of 110 lightning flashes in a certain region resulted in a sample average radar .81 sec. and a sample standard deviation of .34 sec. ("Lightning Strikes to an Airplane in a Thunderstorm," //Journal of Aircraft//, 1984:607-611). Calculate a % (two-sided) confidence interval for the true average echo duration μ, and interpret the resulting interval. ||   ||   ||
 * ||  || 4 ||   || 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 μ and σ^2. ||   ||   ||
 * Homework Set 3b ||  || 5 ||   || Light bulbs of a certain type are advertised as having an average lifetime of 750 hours. The price of these bulbs is favorable, so a potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively determined that the true average lifetime is smaller than what is advertised. A random sample of 50 bulbs was selected, the lifetime of each bulb determined, resulting in the following output: xbar = 738.44, s=38.20. What conclusion would be appropriate at a significance level of .05, A significance level .01? Calculate the p-value of the hypothesis test. What significance level and conclusion would you recommend? ||   ||   ||
 * ||  || 6 ||   || The melting point of each of "' samples of a certain brand of hydrogenated oil was determined, resulting in xBar = 94.32, s = 1.20. Assume that the distribution of melting point is normal distributed. ||
 * Homework Set 4_1 ||  || 1 ||   || Let X denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test ... ||
 * ||  || a ||   || Use the method of moments to obtain an estimate of ϴ and then compute the estimate for this data. ||
 * ||  || b ||   || Obtain the maximum likelihood estimator of ϴ, and then compute the estimate for the given data. ||
 * ||  || 2 ||   || Using data fles, to fit an exponential distribuiton using MOM, ... ||
 * Homework Set 4_2 ||  || 3 ||   || Low-Back Pain (LBP) is a serious health problem in many industrial settings. ... The accompanying summary data on lateral range motion (degrees) for a sample of workers without a history of LBP and another sample with a history of this malady. {Table with Data Provided} ---> Calculate a 90% confidence interval for the difference between population mean extent of lateral movement for the two conditions. Does the interval suggests that population mean lateral motion differs for the two conditions? Is the message different if we use a confidence level of 05%. ||
 * ||  || 4 ||   || In study of cooper deficiency in cattle, the copper values (.g CU/100ml blood) were determined for cattle grazing in an area known to have well defined molybdenum anomalies (metal values in excess of the normal range of regional variation) and for cattle grazing in a non anomalous area ("An investigation into Copper Deficiency in Cattle in the Southern Pennines," J. resulting in s1=21.5,(M=48), for the anomalous condition and s2 = 19.45, (n=45) for the non anomalous condition. Test for the equality of variances versus either one of the populations have the larger variance (using two separate one-sided test) at a significance level of 10% by using the p-value approach.. ||


 * Sources:**
 * EMSE 271, Fall 2009