Let X denote the vibratory stress (psi) on a wind turbine blade at a particular wind speed in a wind tunnel. Use the Rayleigh distribution, with pdf-x2/(282)x >0f(x; 0) = { 02otherwiseas a model for the X distribution.(a) Verify that f(x; 0) is a legitimate pdf.e-x2/(202) dx =82= 0(b) Suppose e = 150. What is the probability that X is at most 200? Less than 200? At least 200? (Round your answer to four decimal places.)at most 200less than 200at least 200(c) What is the probability that X is between 100 and 200 (again assuming e = 150)? (Round your answer to four decimal places.)(d) Give an expression for P(X < x).P(X Sx) =

Answered: Image /qna-images/answer/33d8c689-027d-4afd-9791-3984cd55b9c0.jpg

Answered: Let X denote the vibratory stress (psi)…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Given the two h-scatterplots below, would you say the data is spatially autocorrelated in the direction chosen? Why? h 10 m h 20 m 10 10 024 10 20 NP
Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 43 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 7.50 ml/kg for the distribution of blood plasma. (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limit 1 upper limit 2 margin of error 3 (b) What conditions are necessary for your calculations? (Select all that apply.) n is large the distribution of weights is normal σ is known the distribution of weights is uniform σ is unknown (c) Interpret your results in the context of this problem. 1% of the intervals created using…
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Lorenz curves also can be used to provide a relative measure of the distribution of the total assets of a country. Using data in a report by the economic committee of a certain country, an economist produced the following Lorenz curves for the distribution of total assets in the country in 1963 and 1983, shown below. f(x) = x10 Lorenz curve for 1963 g(x) = x'4 Lorenz curve for 1983 Find the Gini index of income concentration for each Lorenz curve and interpret the results. What is the Gini index for 1963? (Round to three decimal places as needed.) What is the Gini index for 1983? (Round to three decimal places as needed.) Interpret your results. O A. Total assets were more equally distributed in 1963 B. Total assets were more equally distributed in 1983
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4. Let X denote the vibratory stress (psi) on a wind tur- bine 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 X f(x; 0) = { 0² e-x²/(20²) x>0 0 as a model for the X distribution. a. Verify that f(x; 0) is a legitimate pdf. b. Suppose 0 = 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? otherwise c. What is the probability that X is between 100 and 200 (again assuming 0 = 100)? d. Give an expression for P(X ≤ x). 5. A college professor never finishes his lecture before the
Suppose the derivative of a function f(x) is df/dx = (x-8)(x+4)(x-3). Are the below values local minima, local maxima, or neither? x = -8 x = -4 x = 3 x = 12
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Consider the distribution of lifetimes, X(in months) of a particular type of component. The CDF of X isB 1-e**** F(x) ,X > 0 a. Find the pdf of lifetime. b. Find the median of lifetime. c. Find the time t such that 10% of the components fail before t.

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