The following five observations are observed repair times for an airplane engine: 3.6, 23.3, 31.5, 17.9, 4.0. The following questions can be answered independently of each other.
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2
![The following five observations are observed repair times for an airplane engine:
3.6, 23.3, 31.5, 17.9, 4.0.
The following questions can be answered independently of each other.
(a) Assume that the data come from the gamma distribution with mean equal to 10. Use
the method of moments to estimate the shape and scale parameters. [Hint: Write
E(X²) as a function of E(X) and 2.]
(b) Use the Kolmogorov-Smirnov test with type I error 0.10 to assess the hypothesis "the
data come from the gamma distribution with shape parameter equal to 2 and scale
parameter equal to 0.2".](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29082b7a-ec19-42e6-af32-623bfd490a2a%2F3678857d-5533-4734-a213-84d960506e60%2F0rzdsz_processed.jpeg&w=3840&q=75)
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- A manufacturer claims that the tensile strength of a certain composite (in MPa) has the lognormal distribution with μ = 5 and σ = 0.5. Let X be the strength of a randomly sampled specimen of this composite. a) If the claim is true, what is P(X < 20)? b) Based on the answer to part (a), if the claim is true, would a strength of 20 MPa be unusually small? c) If you observed a tensile strength of 20 MPa, would this be convincing evidence that the claim is false? Explain. d) If the claim is true, what is P(X < 130)? e) Based on the answer to part (d), if the claim is true, would a strength of 130 MPa be unusually small? f) If you observed a tensile strength of 130 MPa, would this be convincing evidence that the claim is false? Explain."On average, which value is expected for the F-ratio if the null hypothesis is true?" F = 0 F = k 1 F = N k F = 1The following is part of the computer output from a regression of monthly returns on Waterworks stock against the S&P 500 Index. A hedge fund manager believes that Waterworks is underpriced, with an alpha of 2% over the coming month. Beta R-square Standard Deviationof Residuals 0.75 0.65 0.06 (i.e., 6% monthly) Now suppose that the manager misestimates the beta of Waterworks stock, believing it to be 0.50 instead of 0.75. The standard deviation of the monthly market rate of return is 5%. Required: a. If he holds a $6 million portfolio of Waterworks stock and wishes to hedge market exposure for the next month using one-month maturity S&P 500 futures contracts, what is the standard deviation of the (now improperly) hedged portfolio? The S&P 500 currently is at 3,000 and the contract multiplier is $50. (Do not round intermediate calculations. Round your percentage answer to 2 decimal places.) b. What is the probability of incurring a loss over the next month…
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