a)Let Y₁, Y2,..., Yn denote a random sample of size n taken from a distribution with probabilitydensity function given by :-y-μ1 Вf(y,μ,B)= 2B e0,y>μ and p>0elsewhereAssuming μ = 0, find an estimator, ß for the parameter ß using method of moment.

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Answered: a) Let Y₁, Y2,..., Yn denote a random…

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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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.
1. Let X1,..., X, be a random sample from a distribution with pdf f(x) = 2x, 0< x < 1. Compute the joint density of the smallest and the largest order statisics.
c) Let Y₁, Y₂, ..., Yn be a random sample whose probability density function is given by y3 - formez. 0, f(y; B) = 0 0 elsewhere 200 and suppose that n = 200, Σ²y₁ = 20, ²ºy² 100, i) Derive the standard error of ß, se() = 0.0009, using MLE approach. ii) Find an approximate 95% Confidence interval for B. = y = 250 and Â = 0.025.
Please answer number 3
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?
For a laboratory assignment, if the equipment is working, the density function of the observed outcome X is f(x) = 2x(1-x), 0 < x < 1 Find the variance and standard deviation of X
If needed utilize Moment Generating Functions (MGF), or PGF Please show all steps
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.
9. The random variable X has probability density function, f(x) where k 1
b) Let Y,,Y2, .. , Yn denote a random sample from N(0,0) distribution with probability density function: f(y;8) = e V2n0 i) Show that f(y; 0) belongs to the 1-parameter exponential family. ii) What is the complete sufficient statistic for 0? Justify your answer. iii) Show whether or not, the maximum likelihood estimator is an unbiased estimator of 0. iv) Does the estimator attains the minimum variance unbiased estimator of 0.

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a) Let Y₁, Y2,..., Yn denote a random sample of size n taken from a distribution with probability density function given by : 1 f(y,μ‚ß)= 2B e 0 -y-μ В ,y>μ and p>0 elsewhere Assuming μ = 0, find an estimator, ß for the parameter ß using method of moment.