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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Let X1, , Xn be iid with population density Je (z Sx(x) = r > 0, otherwise. Here 0 is an unkown population parameter. Show that X-0 has an Exponential(1) distribution. Find the method of moment estimator for 0. Let's call this 6. Is ôj unbiased for 0 ? Explain with precise computation. Find the maximum likelihood estimator for 6. Let's call this Ô2. Is ô, unbiased for 0 ? Explain with precise conputation.
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.
please teach this I do not no notations
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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
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.
2.70 Let X and Y be random variables with joint density function (4xy, 0< x,y< 1, f(x,y)= {0, elsewhere. Find the expected value of Z = √X² + y².
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.
Suppose we obtain n observations from a sinusoid contaminated by Gaussian noise: X = A· sin(2 · T· f·k+¢) + Wk, k = 1, 2, ...,n, %3D where Wg are independent identically distributed (iid) Gaussian random variables with mean o and variance o?. The frequency f and phase o are known constants, while A is an unknown constant. Find the maximum likelihood estimator for A. Show all work.
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.
Please answer number 2

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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