Subject TestNote:-You are attempting question 3 out of 12Suppose X ~Binom(4, 0) and define an estimator U =–to estimate e. Then, m4.square error of U is,a)MSE(U) = (1-e)4.b)MSE(U)= 40(1–0)MSE(U) = 0(1–e)%3Dc)%3Dd)MSE (U) = 36e%3DAnswerOABOC2022/1/21 16:32

Answered: Image /qna-images/answer/ace79f4b-1e5d-472f-ab3f-a3670646d9ee.jpg

Answered: 2022/1/21 Suppose X - Binom (4, e) and…

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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Question 4
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
dQ 3Q 20 - dt 100-4t dQ 20 dt 100-t dQ 4Q 100 dt 600 t OP O dt 600 100-4t dQ dt 2Q 50+t 6 - %3D 4Q dQ dt 6. |3D RAD 100-t
Imagine you have two estimators X and Y, for unknown parameter µ. Assume that they are estimated from independent datasets. Let Z = }(X+Y) be the average of these two estimators. To write the symbol µ, you can write mu. For other math notation, you can E[X], Var(X) and (X+Y)/2 or (1/2)(X+Y). Part a - If X and Y are unbiased estimators, E[X] = E[Y] = µ, then is Z unbiased? Explain why or why not. Your explanation should include a short derivation. Part bL Assume Var(X) = Var(Y). Is Z a lower variance or higher variance estimator than X? Explain your answer. Your explanation should include a short derivation.
A WSS process X (t), with mean value 5 and power spectrum Sxx (@) = 50 n. 8 (@) + is applied to a network with impulse response %3D 1+ 2. h (t) = 4. e-4 I %3D (a) Find H (@) of the network (b) Find the Mean and power spectrum of the response Y (t). 3/2
Let {Xi}ni be IID from Bernoulli(p). Find the method of moments estimator of p and use simulations to check whether your estimator is biased or not
Question 7 The following plots have been obtained for a time series. a) Suggest an appropriate ARIMA model based on the below plots. 120- 90- 60- 30- acf 1980 Jan 0.2- 0.1- 0.0 -0.1- 1990 Jan 12 lag [1M] 18 2000 Jan Month pacf 0.2- 0.1- 0.0 -0.1- 2010 Jan 12 lag [1M] 18 2020 Jan 24 h) The following ARIMA output has been obtained from R. Based on this output
Question is in attached image
5- Suppose X1 and X2 are i.id observations from the pdf fa,p (x) = axa-1e-x" logX1 ,x > 0, a > 0 is an ancillarv statistics. logX2 Show that
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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.
Find the method of moments estimators of an non-zero MA(1) process.

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2022/1/21 Suppose X - Binom (4, e) and define an estimator U = to estimate 0. Then, m 4. square error of U is, e(1–0) a) MSE(U) = 4. %3D b) MSE(U)= 40(1-0) %3D c) MSE(U) = 0(1–e) %3D d) MSE (U) = 360 %3D Answer A OB OC