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Let X denote the vibratory stress (psi) on a wind turbine blade at a particular wind speed in a wind tunnel. The article "Blade Fatigue Life Assessment with Application to VAWTS" (J. of Solar Energy Engr., 1982: 107-111) proposes the Rayleigh distribution, with pdf
as a model for the X distribution.
a. Verify that f(x;θ) is a legitimate pdf.
b. Suppose θ = 100 (a value suggested by a graph in the article). What is the probability that X is at most 200? Less than 200? At least 200?
c. What is the probability that X is between 100 and 200 (again assuming θ = 100)?
d. Give an expression for P(X ≤ x).
Obtain a test statistic and p -value. Interpret the results at α = .01.
Find the probability that this shipment is accepted if 5% of the total shipment is defective.
Prove that the probability of exactly n heads in 2n tosses of a fair coin is given by the product of the odd numbers up to 2n - 1 divided by the product of the even numbers up to 2n.
an experimenter wants to conduct a hypothesis test on a claim that there was no difference between two population
A University Web server has five main components each with the same reliability. All five components must work for the server to function as intended.
a) Specify the null and alternate hypotheses for testing that the population correlation is negative. b) Calculate the estimate of the population correlation coefficient between X and Y.
suppose we toss a fair die twice. let e denote the event that the sum of the two tosses is 7 and f denote the event
the correlation between the number of police on the street and the number of crimes committed for a sample of 15
Assess your utility function for automobile life span over the range from 40,000 to 200,000 miles.
the home run percentage is the number of home runs per 100 times at bat. a random sample of 43 professional baseball
What proportion of corks produced by this machine are defective - The specifications call for corks with diameters between 1.9 and 2.1 cm. A cork not meeting the specifications is considered defective.
A field researcher is gathering data on the trunk diameters of mature pine and spruce trees in a certain area. The following are the results of his random sampling. Can he conclude, at the 0.10 level of significance, that the average trunk di..
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