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 withApplication to VAWTS" (J. of Solar Energy Engr., 1982:107-111) proposes the Rayleigh distribution, with pdfe-x²/(20)x> 0f(x; 0) = { 0²0.otherwiseas 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 inthe article). What is the probability that X is at most200? Less than 200? At least 200?с.What is the probability that X is between 100 and 200(again assuming 0 = 100)?d. Give an expression for P(X< x).

Given that : We have to find: a. Verify that f(x; theta) is a legitimate pdf. b. Suppose theta…

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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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a. Find the method of moments (MOM) estimator of θ. b. Is the MOM estimator unbiased?
Consider randomly selecting n segments of pipe and determining the corrosion loss (mm) in the wall thickness for each one. Denote these corrosion losses by Y₁' Yn. The article "A Probabilistic Model for a Gas Explosion Due to Leakages in the Grey Cast Iron Gas Mains"+ proposes a linear corrosion model: Y; = t;R, where t; is the age of the pipe and R, the corrosion rate, is exponentially distributed with parameter 1. Obtain the maximum likelihood estimator of the exponential parameter (the resulting mle appears in the cited article). [Hint: If c> 0 and X has an exponential distribution, so does cX.] O Â = O Â = O λ = * * O n Srit) i = 1 n j = 1 Σ i = 1 n n i = 1 n LY i = 1 n 0 1 = L (rt) 2 i = 1 | = 1 n n Y; | = 1
Do part b in detail
This subject revolves around linear Models. The given problem is attached. I have attempted it but was told to check on Z's range, is my attempt correct?
do part b,c,d
Given: image Find the following: show sol. a) Conditional pdf of Y given X=x b) Conditional Expectation of Y given X=x c) Conditional variance of Y given X=x
An article in the Journal of the American Ceramic Society, "Rapid Hot-Pressing of Ultrafine PSZ Powders" (1991, Vol. 74, pp. 1547-1553) considered the microstructure of the ultrafine powder of partially stabilized zirconia as a function of temperature. The data are shown below: ... x = Temperature (°C) | 1100 1200 1300 1100 1500 1200 1300 y - Porosity (%) 30.8 19.2 6 13.5 11.4 7.7 3.6 Find an estimate of o2 Input answers up to two decimal places. o2= Blank 1
Let X; € {1,2, 3, ...} be the number of days until relapse for patient i who is diagnosed with multiple sclerosis and currently in remission. We model this data using a geometric distribution with pmf iid X1, X2,..., Xn fxp(x | p) = (1 – p)*-'p for 0 < p < 1 defined on x E {1,2, 3, ...} and 0 elsewhere. Here, p is the risk of relapse on each day. 1. Using a p~ Beta(a, B) prior, derive the posterior density of p, fp|X, (p | Xn).
1. The incidence of cancer among phosphate mine workers and their exposure to radiation was investigated. Cancer incidence was recorded among 60 phosphate mine workers who had 0-29 working level months (WLM) of exposure, 60 phosphate mine workers who had 30-89 WLM of exposure, and 60 phosphate mine workers who had 90-120 WLM of exposure. The number of cancer incidences for each group are presented in Table 1. Table 1: Two-way Table of Counts Cancer Incidence Exposure Level Yes No Total 0-29 WLM 20 40 60 30-89 WLM 33 27 60 90-120 WLM 43 17 60 Total 96 84 180 Perform a x? test, at the 5% level of significance, whether cancer incidence rates differ between the three levels of radiation among phosphate mine workers.
2.11 Let X have the standard normal pdf, fx(x) = (1/√√2π) e¯2²/² (a) Find EX² directly, and then by using the pdf of Y = X2 from Example 2.1.7 and calculating EY. (b) Find the pdf of Y = |X|, and find its mean and variance.
c) Consider the following table: i 1 2 3 4 5 6 7 8 9 10 R₁ 0.7329 0.9755 0.6761 0.0917 0.1584 0.2858 0.8564 0.3628 0.4337 0.5822 Assuming an M/M/1 setup, a service rate of 18 customers every 5 minutes, and a traffic intensity of 0.95 for a pdf characterized by the exponential distribution, compute the correpsonding variates.
5.1-1

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