The standard deviation of lifetimes is known to be 100 hours. A random sample of 64 bulbs from the shipment results in a sample mean lifetime of X = 350 hours. Let $X$ be the height of a randomly chosen individual from a population. &=\frac{a \theta+b-b}{a}\\ \textrm{Var}(\hat{\Theta}_n)&=E\left[\hat{\Theta}_n^2\right]- \big(E[\hat{\Theta}_n]\big)^2\\ \lim_{n \rightarrow \infty} MSE(\hat{\Theta}_n)=\lim_{n \rightarrow \infty} \frac{2\theta^2}{(n+2)(n+1)}=0. \begin{align}%\label{} Well, first of all, we need to do the basics: Acquire training and skilling up your PMs / BAs in cost estimation – Analogous (or Parametric) estimating – Bottom-up … Thus, by, If $X_i \sim Geometric(\theta)$, then Whether a web development project is big or small, a good project estimation can make things easier during the project execution cycle. Let $X_1$, $X_2$, $X_3$, $...$, $X_n$ be a random sample from a $Geometric(\theta)$ distribution, where $\theta$ is unknown. \frac{d \ln L(x_1, x_2, \cdots, x_n; \theta)}{d\theta}= \bigg({\sum_{i=1}^n x_i-n} \bigg) \cdot \frac{-1}{1-\theta}+ \frac{n} {\theta}. \end{array} \right. \end{align} \begin{align} 0000077588 00000 n E\left[\hat{\Theta}_n^2\right]&= \int_{0}^{\theta} y^2 \cdot \frac{ny^{n-1}}{\theta^n} dy \\ &=\frac{n}{n+2} \theta^2. \begin{align} \hat{\Theta}_2=\frac{\hat{\Theta}_1-b}{a} If ˆΘ1 is an estimator for θ such that E[ˆΘ1] = aθ + b, where a ≠ 0, show that ˆΘ2 = ˆΘ1 − b a. is an unbiased estimator for θ. 1. The QC manager at a light bulb factory needs to estimate the average lifetime of a large shipment of bulbs made at the factory. If $\hat{\Theta}_1$ is an unbiased estimator for $\theta$, and $W$ is a zero mean random variable, then, Let $X_1$, $X_2$, $X_3$, $...$, $X_n$ be a random sample from a $Uniform(0,\theta)$ distribution, where $\theta$ is unknown. Therefore, &=\frac{n}{n+1} \theta. Keywords: approximation error, differences of numerical solutions, Inverse Problem, Tikhonov regularization, Euler equations. We obtain the following values (in centimeters): Find the values of the sample mean, the sample variance, and the sample standard deviation for the observed sample. (Note that Z=1.645 to reflect the 90% confidence level.) Access Parameter Estimation and Inverse Problems 3rd Edition Chapter 3 Problem 3EX solution now. Measurement and Geometry 26%. \end{align} For $i=1,2,...,n$, we need to have $\theta \geq x_i$. Define the estimator. \nonumber F_X(x) = \left\{ 0000000827 00000 n \begin{align} EstimatingMargin Methods &Algorithms LikelihoodEquations/MLE REML Comparison Algorithms Problems Summary Methods and Algorithms (continued) An estimation method yields the … \end{array} \right. You might 0000001340 00000 n Please ask questions!!! ˆΘ2 = ˆΘ1 + W is also an unbiased estimator for θ. \nonumber f_X(x) = \left\{ Thus, So how do we approach these problems with cost estimation and what is the PMO’s role in the solution? 0000059883 00000 n H��Wێ�F}�W�CP����Y��&�����yhQ-�=R! \end{align} Testberichte zu Parameter estimation and inverse problems solution manual analysiert. Computation and Estimation. \end{align}. Therefore, the MLE can be written as We will see an example of such scenarios in the Solved Problems section (Section 8.2.5). Thus, $X_i$'s are i.i.d. P_{X_i}(x;\theta) = (1-\theta)^{x-1} \theta. \end{align} ← 0000005736 00000 n \end{align} \begin{array}{l l} \begin{array}{l l} Welche Punkte es vor dem Kauf Ihres Parameter estimation and inverse problems solution manual zu beurteilen gibt! Note that $\frac{1}{\theta^n}$ is a decreasing function of $\theta$. \begin{align}%\label{} & \quad \\ By, To find the bias of $\hat{\Theta}_n$, we have Is $\hat{\Theta}_n$ a consistent estimator of $\theta$? 26%. \frac{1}{\theta} & \quad 0 \leq x \leq \theta \\ 0000003182 00000 n Problems and Solutions for Density Estimation In this lecture we consider ways to improve density estimation. Sämtliche in der folgenden Liste beschriebenen Parameter estimation and inverse problems solution manual sind 24 Stunden am Tag auf Amazon im Lager und extrem schnell bei Ihnen zuhause. \hat{\theta}_{ML}= \max(x_1,x_2, \cdots, x_n). 24%. Project Cost Estimate Problems and Approach to a Solution Posted by: Laith Adel on March 15, 2017 In order to understand the cost estimates problems, we need … Thus, the bias is given by \end{align} 26% \end{align}, To find $MSE(\hat{\Theta}_n)$, we can write & \quad \\ &= \frac{n}{n+1} \theta-\theta\\ Project estimation is one of the most important steps in project management. Site Navigation. \end{align} \end{align} We have Linearity in Instrumental Variables Estimation: Problems and Solutions* The linear IV estimator, in which the dependent variable is a linear function of a potentially endogenous regressor, is a major workhorse in empirical economics. Then, the log likelihood function is given by Equipment $ 9,000,000 NOWC … \begin{align} By setting the derivative to zero, we can check that the maximizing value of $\theta$ is given by \end{array} \right. \end{align}. Solutions to Selected Problems. This often means drawing on everyday facts and numbers that you know to work out something that you probably hadn’t thought about before. Project Cost Estimation: Issues and the Possible Solutions. and the true error, obtained by subtraction of numerical and analytic solutions, is presented. 0000006719 00000 n Even for the estimation of the simplest chlorophyll fluorescence parameter, F v /F m, some additional protocol such as addition of DCMU or illumination of weak blue light is necessary. Find the bias of $\hat{\Theta}_n$, $B(\hat{\Theta}_n)$. )k���?����E�&����⥺��S��]-^�V���.�����?|ڵ�V�9-Z�>r�Ȅ���w}|��Ž�z���W��X�YQ���;�v�oOB�X7��k;�,:UW��E� Problem-solving: Estimation problems - Solutions Dr Kathryn Boast, Hertford College 29th June 2020 Introduction Estimation problems, as their name suggests, ask you to estimate something. &=\textrm{Var}(\hat{\Theta}_n)+ \frac{\theta^2}{(n+1)^2}. Carl needs to buy 144 tiles, and each box contains 5 tiles. \begin{align} &=f_{X_1}(x_1;\theta) f_{X_2}(x_2;\theta) \cdots f_{X_n}(x_n;\theta)\\ trailer << /Size 38 /Info 12 0 R /Root 15 0 R /Prev 91688 /ID[<706b73a2285cbd0b4e9d514a3c865238><348bb13a8239ac31172e666a142edcc9>] >> startxref 0 %%EOF 15 0 obj << /Type /Catalog /Pages 11 0 R /Metadata 13 0 R /PageLabels 10 0 R >> endobj 36 0 obj << /S 95 /L 170 /Filter /FlateDecode /Length 37 0 R >> stream 5216 September 2010 IZA P.O. Solution. \end{align} &=\left\{ Estimating answers to problems can be necessary if the calculations are to complex to perform or if you need a quick answer (that does not have to be exact). \begin{align}%\label{} If $X \sim Uniform (0, \theta)$, then the PDF and CDF of $X$ are given by Thus, the likelihood function is given by Thus, the smallest possible value for $\theta$ is Corresponding Author *Jim Bouldin, Department of Plant Sciences, 1210 PES Building, Mail Stop 1, University of California at Davis, Davis, CA 95616, USA. Box 7240 53072 Bonn Germany Phone: +49-228-3894-0 Fax: +49-228-3894-180 E-mail: iza@iza.org Any opinions expressed here are those of the author(s) and not those of IZA. Thus, $\hat{\Theta}_2$ is an unbiased estimator for $\theta$. Budgeted sales ( $10 per unit) $2,60,000 p.a. 0000002693 00000 n Ich empfehle Ihnen stets zu erforschen, ob es bereits Erfahrungen mit dem Produkt gibt. \end{align} Thus, we need to find $\textrm{Var}(\hat{\Theta})$. Parameter estimation and inverse problems solution manual - Unser Favorit . Some problems and solutions in density estimation from bearing tree data: a review and synthesis. Thus, the MLE can be written as About. 14 0 obj << /Linearized 1 /O 16 /H [ 920 266 ] /L 92096 /E 77944 /N 2 /T 91698 >> endobj xref 14 24 0000000016 00000 n Maximum likelihood is defined, and its association with least squares solutions under normally distributed data errors is demonstrated. Find the maximum likelihood estimator (MLE) of $\theta$ based on this random sample. The process of estimation is carried out in order to measure and diagnose the true value of a function or a particular set of populations. 1. Estimation problems Cristiano Porciani AIfA, Bonn. E[\hat{\Theta}_2]&=E[\hat{\Theta}_1]+E[W] & (\textrm{by linearity of expectation})\\ \end{align} L(x_1, x_2, \cdots, x_n; \theta)&=f_{X_1 X_2 \cdots X_n}(x_1, x_2, \cdots, x_n; \theta)\\ \end{align} Updates/Reminders; Prerequisites: EE 224, EE 322, Basic calculus & linear alegbra.Suggested class to also take: EE 523; Location, Time: Marston 204, Tues-Thurs 2:10-3:30pm Instructor: Prof Namrata Vaswani Office Hours: Monday 11-12, Tuesday 10-11, or by appointment, or stop by after 4pm to check if … MSE(\hat{\Theta}_n)&=\frac{n}{(n+2)(n+1)^2} \theta^2+ \frac{\theta^2}{(n+1)^2}\\ Estimation is a division of statistics and signal processing that determines the values of parameters through measured and observed empirical data. a. So, the 90% confidence interval is (126.77, 127.83) ===== Answer to BMI Problem on page 3. Correct! Sparse Estimation of Spectral Lines: Grid Selection Problems and Their Solutions Abstract: Grid selection for sparse estimation of spectral-line parameters is a critical problem that was in need of a satisfactory solution: assuming the usual case of a uniform spectral grid how should one select the number of grid points, K? Sales p D E H \begin{array}{l l} ��z]��D����qL�j�#�Lr����.�j/�������K. Various cost estimation methods are available for use in software development process but concern lies in selecting better software cost estimation model to arrive at accurate cost estimation. \end{align} the working capital requirements. &= \sqrt{S^2}=6.1 0000001165 00000 n Maximum Likelihood Estimation Linear regression is introduced as a parameter estimation problem, and least squares solutions are derived. \begin{align} Most have been written for examinations ESE 524 or its pre-decessor EE 552A at Washington University in St. … Keywords: approximation error, differences of numerical solutions, Inverse Problem, Tikhonov regularization, Euler equations. 0000002915 00000 n &=\frac{n}{(n+2)(n+1)^2} \theta^2. My coordinates •Cristiano Porciani, Argelander Institute für Astronomie, Auf dem Hügel 71, D-53121, Bonn •porciani@astro.uni-bonn.de •Cosmology, large-scale structure of the universe, intergalactic medium . and 0000006566 00000 n Ehrliche Bewertungen durch Dritte geben ein aufschlussreiches Bild bezüglich der Wirksamkeit ab. Estimation is the process of using approximations to get a "close enough" answer. The numerical stability of these three-point perspective solutions are discussed. In this document, problems in detection and estimation theory are collected. \begin{align} Even for the estimation of the simplest chlorophyll fluorescence parameter, F v /F m, some additional protocol such as addition of DCMU or illumination of weak blue light is necessary. \nonumber f_X(x) = \left\{ E[\hat{\Theta}_2]&=\frac{E[\hat{\Theta}_1]-b}{a} (\textrm{by linearity of expectation})\\ %PDF-1.3 %���� 0 & \quad \text{otherwise} & \quad \\ Betas may vary over time • 2. \end{align} Use estimation to solve multi-step word problems involving addition, subtraction, multiplication, and division. \begin{align} \begin{align} Let $X_1$, $X_2$, $X_3$, $...$, $X_n$ be a random sample from a $Uniform(0,\theta)$ distribution, where $\theta$ is unknown. 0 & \quad x<0 \\ Estimation is the process of obtaining reasonably accurate answers through making educated guesses. \end{align} \end{align}, Note that Problems in Cash Flow Estimation in Financial Management - Problems in Cash Flow Estimation in Financial Management courses with reference manuals and examples pdf. 0000040389 00000 n Even if $\theta$ is a real-valued parameter, we cannot always find the MLE by setting the derivative to zero. Sparse Estimation of Spectral Lines: Grid Selection Problems and Their Solutions Abstract: Grid selection for sparse estimation of spectral-line parameters is a critical problem that was in need of a satisfactory solution: assuming the usual case of a uniform spectral grid … Estimation problems deal with how best to estimate the What are the information did you get from the problem? Estimation of Beta Beta Estimation: Problems and Solutions Problems • 1. \begin{align}%\label{eq:union-bound} Practice: 2-step estimation word problems. Analysis and solutions of the three point perspective pose estimation problem Abstract: The major direct solutions to the three-point perspective pose estimation problems are reviewed from a unified perspective. We have \begin{align} If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. \ln L(x_1, x_2, \cdots, x_n; \theta)= \bigg({\sum_{i=1}^n x_i-n} \bigg) \ln (1-\theta)+ n \ln {\theta}. What is the 90% confidence interval for BMI? Sample size may be inadequate • 3. Number and Number Sense . \begin{align}%\label{} 1 One and two sample estimation problems The distributions associated with populations are often known except for one or more parameters. More Estimation Practice Problems and Solutions 1. In this review, those problems in the measurements of chlorophyll fluorescence in cyanobacteria are introduced, and solutions to those problems are given. & \quad \\ 0000009396 00000 n Next lesson. \frac{1}{\theta^n} & \quad 0 \leq x_1, x_2, \cdots, x_n \leq \theta \\ 0 & \quad \text{otherwise} \end{align} Interval Estimation Questions and Answers Test your understanding with practice problems and step-by-step solutions. Problem 2: Straight Line Method. Our solutions are written by Chegg experts so you can be assured of the highest quality! By rounding numbers, you can easily find answers to complex multiplication and division problems that you would otherwise be unable to solve. d) solve single-step and multistep addition, subtraction, and multiplication problems with whole numbers. 0000001186 00000 n Research published in this series may include views on … Betas are influenced by changing leverage and business risk Solutions • 1 and 2. Solutions to Estimation Problems for Scalar Hamilton–Jacobi Equations Using Linear Programming Christian G. Claudel, Member, IEEE, Timothée Chamoin, and Alexandre M. Bayen, Member, IEEE Abstract—This brief presents new convex formulations for solving estimation problems in systems modeled by scalar Hamilton–Jacobi (HJ) equations. \hat{\Theta}_{ML}= \max(X_1,X_2, \cdots, X_n). &=P_{X_1}(x_1;\theta) P_{X_2}(x_2;\theta) \cdots P_{X_n}(x_n;\theta)\\ &=(1-\theta)^{\left[\sum_{i=1}^n x_i-n\right]} \theta^{n}. The numerical stability of these three-point perspective solutions are discussed. Introduction The need for the reliable numerical methods at modeling of problems governed by systems of partial differential equations (PDE) causes the interest to the verification of software and numerical solutions that stimulates the development of methods for … \begin{align}%\label{} Answer to first problems on page 3. \begin{align} 0000000920 00000 n For example, the maximum might be obtained at the endpoints of the acceptable ranges. (i) In total and (ii) As regards each constituent part of working capital. \begin{align} \begin{align}%\label{} Note that this is one of those cases wherein $\hat{\theta}_{ML}$ cannot be obtained by setting the derivative of the likelihood function to zero. When this regressor takes on multiple values, the linear specification restricts the marginal effects to be constant We have 1 & \quad x>1 Bias at the Boundary of the Distribution Many distributions have bounded support, that is, the range of val-ues for which f(y) > 0 is bounded. Probability, Statistics, Patterns, Functions, and Algebra. Solve for the annual depreciation. Here, the maximum is achieved at an endpoint of the acceptable interval. \begin{align} Statistical tests based on χ 2 that provide insight into least squares solutions are discussed. &=\theta. \end{align} 0000001511 00000 n B(\hat{\Theta}_n)&=E[\hat{\Theta}_n]-\theta \\ \begin{array}{l l} 0000059610 00000 n Jim Bouldin. This is the currently selected item. 0 & \quad \text{otherwise} A Fast and Accurate Solution for Pose Estimation from 3D Correspondences Lipu Zhou, Shengze Wang, and Michael Kaess Abstract—Estimating pose from given 3D correspondences, including point-to-point, point-to-line and point-to-plane corre-spondences, is a fundamental task in computer vision with many applications. 0000006239 00000 n If you're seeing this message, it means we're having trouble loading external resources on our website. Solutions to Problem Set #6: Demand Estimation and Forecasting 1) Consider the following regression for Ice Cream sales (in thousands) as a function of price in dollars per pint. \begin{align}%\label{} Browse through all study tools. Alles was auch immer du also beim Begriff Parameter estimation and inverse problems solution manual erfahren möchtest, findest du auf der Seite - ergänzt durch die ausführlichsten Parameter estimation and inverse problems solution manual Tests. If each box contains 5 tiles, estimate the total number of boxes of tiles Carl should buy. \begin{align} &=\theta. &=168.8 Let's try solving a division word problem! Introduction The need for the reliable numerical methods at modeling of problems governed by systems Estimation problems Cristiano Porciani AIfA, Bonn. \frac{x}{\theta} & \quad 0 \leq x \leq \theta \\ We have E [ ˆ Θ 2] = E [ ˆ Θ 1] + E [ W] ( by linearity of expectation) = θ + 0 ( since ˆ Θ 1 is unbiased and E W = 0) = θ. In this review, those problems in the measurements of chlorophyll fluorescence in cyanobacteria are introduced, and solutions to those problems are given. Find the maximum likelihood estimator (MLE) of $\theta$ based on this random sample. These problems are primarily written by Professor Joseph A. O’Sullivan. &=\frac{2\theta^2}{(n+2)(n+1)}. Donate or volunteer today! The likelihood function is given by Software Project Cost Estimation: Issues, Problems and Possible Solutions Adanma C. Eberendu ABSTRACT : Software project managers have expressed concern over their inability to estimate … Estimation is the process of extrapolating from known information to unknown, in order to get close to the correct answer. \end{align} Our mission is to provide a free, world-class education to anyone, anywhere. Im Folgenden finden Sie als Kunde unsere Liste der Favoriten an Parameter estimation and inverse problems solution manual, bei denen Platz 1 unseren Testsieger ausmacht. \begin{align} 2-step estimation word problems. Estimation: Problems and Solutions Magne Mogstad Statistics Norway and IZA Matthew Wiswall New York University Discussion Paper No. Estimating Division Word Problems. \end{align} \hat{\Theta}_{ML}= \frac{n} {\sum_{i=1}^n X_i}. L(x_1, x_2, \cdots, x_n; \theta)&=P_{X_1 X_2 \cdots X_n}(x_1, x_2, \cdots, x_n; \theta)\\ Solution. News; It is shown that even in cases where the solution is not near the geometric unstable region considerable care must be exercised in the calculation. \begin{align} 0000005958 00000 n 0000002132 00000 n My coordinates •Cristiano Porciani, Argelander Institute für Astronomie, Auf dem Hügel 71, D-53121, Bonn •porciani@astro.uni-bonn.de •Cosmology, large-scale structure of the universe, intergalactic medium. \end{align} \overline{X}&=\frac{X_1+X_2+X_3+X_4+X_5+X_6+X_7}{7}\\ &= -\frac{\theta}{n+1}. Least squares problems How to state and solve them, then evaluate their solutions Stéphane Mottelet Université de Technologie de Compiègne April 28, 2020 Stéphane Mottelet (UTC) Least squares 1/63. Find the MSE of $\hat{\Theta}_n$, $MSE(\hat{\Theta}_n)$. Kernel density estimators have a … {S}^2=\frac{1}{7-1} \sum_{k=1}^7 (X_k-168.8)^2&=37.7 0000003143 00000 n One and two-step word problems. Thus, Khan Academy is a 501(c)(3) nonprofit organization. Chapter 12: Cash Flow Estimation and Risk Analysis Answers and Solutions 51 Solutions to End-of-Chapter Problems 12-1 a. In order to estimate the mean and variance of $X$, we observe a random sample $X_1$,$X_2$,$\cdots$,$X_7$. The following MATLAB code can be used to obtain these values: If $\hat{\Theta}_1$ is an estimator for $\theta$ such that $E[\hat{\Theta}_1]=a \theta+b$, where $a \neq 0$, show that and have the same distribution as $X$. The first cost of a machine is Php 1,800,000 with a salvage value of Php 300,000 at the end of its six years of life. &=\theta+0 & (\textrm{since $\hat{\Theta}_1$ is unbiased and } EW=0)\\ \begin{align} H�b```���7@(�������з��m@�1M3Y�t0#c��y'000 & \quad \\ My data is taken from multiple location at one point in time. Thus, to maximize it, we need to choose the smallest possible value for $\theta$. 0000070156 00000 n Analysis of Costs $ MSE(\hat{\Theta}_n)&=\textrm{Var}(\hat{\Theta}_n)+B(\hat{\Theta}_n)^2\\ Thus, $\hat{\Theta}_2$ is an unbiased estimator for $\theta$. E[\hat{\Theta}_n]&= \int_{0}^{\theta} y \cdot \frac{ny^{n-1}}{\theta^n} dy \\ \end{array} \right. \hat{\theta}_{ML}= \frac{n} {\sum_{i=1}^n x_i}. Abstract: The major direct solutions to the three-point perspective pose estimation problems are reviewed from a unified perspective. C.J.Anderson (Illinois) Estimation: Problems&Solutions Spring2020 10.10/ 100. Please ask questions!!! &=\frac{166.8+171.4+169.1+178.5+168.0+157.9+170.1}{7}\\ If $X_i \sim Uniform(0,\theta)$, then Many times a project’s success or failure depends on the proper estimation … Unsere Redaktion wünscht Ihnen als Kunde hier viel Spaß mit Ihrem Parameter estimation and inverse problems solution manual! Carl needs to buy 144 tiles for his bathroom. 0000009474 00000 n \frac{1}{\theta} & \quad 0 \leq x \leq \theta \\ \end{align} Jttt@Tt�@X�00�l �"@, Qg�gx�$ d��@쁾�e��슞8��y�c�2��s���~ц-L|P[9��A��'@� Wy%\ endstream endobj 37 0 obj 154 endobj 16 0 obj << /Type /Page /Parent 11 0 R /Resources 17 0 R /Contents 23 0 R /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 17 0 obj << /ProcSet [ /PDF /Text ] /Font << /TT2 18 0 R /TT4 19 0 R /TT6 25 0 R /TT7 27 0 R >> /ExtGState << /GS1 29 0 R >> /ColorSpace << /Cs6 22 0 R >> >> endobj 18 0 obj << /Type /Font /Subtype /TrueType /FirstChar 32 /LastChar 177 /Widths [ 250 333 0 0 500 833 0 0 333 333 0 0 250 333 250 278 500 500 500 500 500 500 500 500 500 500 278 0 0 564 0 444 0 722 0 667 0 0 556 0 0 333 0 722 0 0 722 722 556 722 667 556 611 722 0 944 0 722 0 0 0 0 0 0 0 444 500 444 500 444 333 500 500 278 278 500 278 778 500 500 500 500 333 389 278 500 500 722 500 500 444 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 333 444 444 0 500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 549 ] /Encoding /WinAnsiEncoding /BaseFont /CEAONH+TimesNewRoman /FontDescriptor 21 0 R >> endobj 19 0 obj << /Type /Font /Subtype /TrueType /FirstChar 32 /LastChar 177 /Widths [ 250 0 0 0 0 0 0 0 333 333 0 0 250 0 250 0 500 500 500 500 500 500 500 500 0 500 0 0 0 0 0 0 0 722 667 0 0 667 0 0 0 0 0 0 0 944 0 0 611 0 0 556 667 0 0 0 0 0 0 0 0 0 0 0 0 500 556 444 556 444 333 0 0 278 0 0 278 833 556 500 0 0 444 389 333 556 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 549 ] /Encoding /WinAnsiEncoding /BaseFont /CEAPCH+TimesNewRoman,Bold /FontDescriptor 20 0 R >> endobj 20 0 obj << /Type /FontDescriptor /Ascent 891 /CapHeight 656 /Descent -216 /Flags 34 /FontBBox [ -558 -307 2034 1026 ] /FontName /CEAPCH+TimesNewRoman,Bold /ItalicAngle 0 /StemV 133 /FontFile2 31 0 R >> endobj 21 0 obj << /Type /FontDescriptor /Ascent 891 /CapHeight 656 /Descent -216 /Flags 34 /FontBBox [ -568 -307 2028 1007 ] /FontName /CEAONH+TimesNewRoman /ItalicAngle 0 /StemV 94 /XHeight 0 /FontFile2 30 0 R >> endobj 22 0 obj [ /ICCBased 28 0 R ] endobj 23 0 obj << /Length 2479 /Filter /FlateDecode >> stream The sample variance is given by Determine the total depreciation after three years using the Straight Line Method of Depreciation. Finally, the sample standard deviation is given by