Ук.Suppose that Y₁. Y₂; Yn 15.2fromFunctionrandomSamplea population with probability densityf(y) =find the maximumBY1-BBlike hoodozy 21: B >0ElsewhereEstimatorof B

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Answered: Suppose that Y; Y₂; Yn is random Sample…

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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Suppose that X1,.…,X, is a random sample from the Gamma distribution with |density .... f(t; α, β ) = r(a)* r >0 and parameters a, B > 0. Using the fact, without proof, that the expected value and variance of the Gamma distribution are given by a/ß and a/32, respectively, find the method-of-moment estimator of a and B.
2.1. Let X1, X2. .... Xm denote a random sample from the exponential density with mean , and let Y,, Y2. ... Y, denote an independent random sample from an exponential density with mean 02. Find the likelihood ratio criterion for testing Họ: 0, = 02 versus Hạ: 0z # 02.
c) Let Y₁, Y₂,..., Yn be a random sample whose probability density function is given by f(v:B)= 684 - fa 00 0, elsewhere 200 200 200 and suppose that n = 200, y = 20, y = 100, y = 250 and $ = 0.025. i=1 i) Derive the standard error of ß, se(B) = 0.0009, using MLE approach. ii) Find an approximate 95% Confidence interval for B.
E2
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two random independant variables X and Y with distributions: X ∼ Poisson(λ) og Y ∼ Poisson(2λ), andobservations x = 2 og y = 5 .(a) What is the log-likelihood function? b) calculate MLE for the observated samples
Problem 3 A team of mechanical engineering students is analyzing tensile strength of bars used to build a model truss bridge. An instructor tells the students that tensile strength is approximately normally distributed with variance o² = 500 N². A random sample of 25 bars has a mean tensile strength of x = 1025 N. a) Construct a 99% two-sided Cl on mean tensile strength. b) Compare the width of the 99% CI with the width of the 95% CI: that is, evaluate and report the width of 99% CI ratio width of 95% CI
Let Y1, Y2,..., Y, denote a random sample from the density function given by 1 yª-'e=y/®, y> 0, f(y[a, 0) = elsewhere, where a > 0 is known. a Find the MLE Ô of 0. b Find the expected value and variance of ê. c. Is the MLE ô an unbiased estimator for 0?
b) Let X to be a random sample from a distribution with a probability density function given by f(x; 0) = {0x0-¹,if 0 i) Find the level of significance of the test, a. ii) Calculate the power of the test.
13. Let (x1, 12, .., an) be a random sample on the random variable X with density function f(x) = ae¯a(z-B), x > B, a, B > 0 %3D (a) Find the maximum likelihood estimators of a and B. (b) If the sample values are; 5.3 5.1 7.2 5.5 6.1 5.3 6.1 5.9 5.5 6.5 find the maxi- mum likelihood estimates of a and B.
20. The quantity demanded (in thousands of pounds) of a Red Farms Butter each week is a contniuouis 1 1 2 36 random variable with probability density function (PDF): f(x)=x -x² (0≤x≤6). a) Show that it is a PDF on the specified interval. b) What is the probability that between 3-4 thousand pounds of butter will be demanded in a randomly selected week?
a) Suppose that X is a random variable having the following probability density function given by (2(0-x) 02 f(x) = -, x > 0 (0, elsewhere Find the value of c such that an interval from x to cx is a (1- a)100% confidence interval for the parameter 0.

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Suppose that Y; Y₂; Yn is random Sample from a population with probability density Function find the foy fap = maximum B 1-B B y like hood ozy 21:8 >0 Elsewhere of B Estimator of