Engineering Probability and Statistics

Practice Exam Môn Engineering Probability and Statistics. Tài liệu được sưu tầm gồm 6 trang, giúp bạn ôn tập tốt hơn. Mời các bạn đón xem. 

Final Exam Môn Engineering Probability and Statistics. Tài liệu được sưu tầm gồm 8 trang, giúp bạn ôn tập tốt hơn. Mời các bạn đón xem. 

A tennis tournament with knockout format is arranged for 8 players will consist of quarterfinal round, semifinal round, and a grand final match. In any match either player has a probability 0.50 of winning. Assume we have two specific player called Djokovic and Federer among the players. a) What is the probability that they meet each other in the semi-finals? (5 pts) b) What is the probability that they meet each other in the grand final? (5 pts). Tài liệu giúp bạn tham khảo, ôn tập và đạt kết quả cao. Mời bạn đón xem.

A man has 2 coins, one is fair coin and one is 2-head coin. He randomly picks a coin and toss it. a) Find the probability that the face up value is Head (5 pts) Let C1 be the event that he chooses a regular coin and let C2 be the event that he chooses the two-headed coin. Note that C1 and C2 form a partition of the sample space. We already know that P(H|C1)=0.5, P(H|C2)=1. Thus, we can use the law of total probability to write P(H) = P(H|C1) x P(C1) + P(H|C2) x P(C2) = =. Tài liệu giúp bạn tham khảo, ôn tập và đạt kết quả cao. Mời bạn đón xem.

A 1st process creates shafts with defective rate 20%. For each defective item, we lost $2. The company is considering the 2nd process. In this process, shafts can be machined twice. In the 1st step, the diameter of the shaft in follows normal distribution with parameters N 100. Shafts satisfying the tolerance are not machined again. Shafts which are reparable, i.e., at first their diameters are not lied within the tolerance but they can be machined again to satisfy the tolerance, are turned the second time. This 2nd machining costs 0.3 for each shaft. The rest is classified as irreparable. Tài liệu giúp bạn tham khảo, ôn tập và đạt kết quả cao. Mời bạn đón xem.

Assume that the number of defect screws in a box follows Poisson distribution with ! = 2. The box will pass the quality test if number of defect screw is smaller or equal to 3. a) Find the probability passing the quality test of a box. (7pts) b) In stead of checking each box, now two boxes are combined as a package. A package will pass the quality test if number of defect screws is smaller or equal to 6. Find the probability passing the quality test of a package. (8pts). Tài liệu giúp bạn tham khảo, ôn tập và đạt kết quả cao. Mời bạn đón xem.

To estimate μ, the average nicotine content of a newly marketed cigarette, 25 of these cigarettes are randomly chosen, and their nicotine contents are determined. It is known from past experience that the standard deviation of the nicotine content of a cigarette is equal to 0.8 milligrams. If the average nicotine finding is 1.74 milligrams, what is a 90% confidence interval estimator of μ? (20p). Tài liệu giúp bạn tham khảo, ôn tập và đạt kết quả cao. Mời bạn đón xem.

Given that the two dice land on different numbers, find the conditional probability that at least one die roll is a 5. (5 pts) Let A be the event that at least one die is a 5 and B be the event that two dice land on different numbers. We are going to compute Pr[A|B] = Simply enumerating out the possibilities, we see that Pr[A∩B] = = and Pr[B] = = . So, Pr[A|B] = =. Tài liệu giúp bạn tham khảo, ôn tập và đạt kết quả cao. Mời bạn đón xem.

The tensile strength of Portland cement is being studied. Four different mixing techniques can be used economically. A completely randomized experiment was conducted and the following data were collected: Analyze the data from this experiment (use α=0.05) and draw conclusions. A study was performed on wear of a bearing y and its relationship to x1 oil viscosity and x2 load. The following data were obtained. Tài liệu giúp bạn tham khảo, ôn tập và đạt kết quả cao. Mời bạn đón xem.

An economist thinks that at least 60 percent of recently arrived immigrants who have been working in the health profession in the United States for more than 1 year feel that they are underemployed with respect to their training. Suppose a random sample of size 450 indicated that 294 individuals (65.3 percent) felt they were underemployed. Is this strong enough evidence to prove that the economist is correct? Tài liệu giúp bạn tham khảo, ôn tập và đạt kết quả cao. Mời bạn đón xem.