## Statistics And Numerical Methods

 Newton polynomial interpolation Lagrange polynomial interpolation is particularly convenient when the same values V0, V1, ... Vn are repeatevely used in several applications. The data values can be stored in computer memory and number of computations can thus be reduced. Limitations of the Lagrange interpolation occur when additional data points are added or removed to improve the appearance of the interpolating curve.
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 Lagrange's Interpolation Formula This is again an Nth degree polynomial approximation formula to the function f(x), which is known at discrete points xi, i = 0, 1, 2 . . . Nth. The formula can be derived from the Vandermonds determinant but a much simpler way of deriving this is from Newton's divided difference formula
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 Taylor Series Before you start this module, you must know how to find the Taylor polynomials of a given function. You should also be familiar with the geometric series, the notion of a power series, and in particular the concept of the radius of convergence of a power series.
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 Sampling Distributions The method we will employ on the rules of probability and the laws of expected value and variance to derive the sampling distribution.
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 Numerical Integration After transformation to a canonical element  typical integrals in the element stiness,or mass matrices  have the forms.
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 Finite Difference Methods Basics Examples of differential equations in one space dimension,General linear second order partial differential equations
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 Newton-Raphson Method You are working for ‘DOWN THE TOILET COMPANY’ that makes floats for ABC commodes. The floating ball has a specific gravity of 0.6 and has a radius of 5.5 cm. You are asked to find the depth to which the ball is submerged when floating in water
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 Newton's Interpolation Formulae As stated earlier, interpolation is the process of approximating a given function
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 Iterative Methods For Solving Linear System As a numerical technique, Gaussian elimination is rather unusual because it is direct. That is, a solution is obtained after a single application of Gaussian elimination. Once a “solution” has been obtained, Gaussian elimination offers no method of refinement.
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 Interview Questions Regardless of your age, interviewing for a job is often challenging. Even mid-career and older workers who have had considerable experience interviewing employees, describe their own encounters as an applicant as “stressful and tedious”.
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 Hypothesis Testing: Single Mean One job of a statistician is to make statistical inferences about populations based on samples taken from the population. Confidence intervals are one way to estimate a population parameter. Another way to make a statistical inference is to make a decision about a parameter
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 Generalized Jacobi and Gauss-Seidel Methods The Jacobi and Gauss-Seidel algorithms are among the stationary iterative methods for solving linear system of equations. They are now mostly used as preconditioners for the popular iterative solvers. In this paper a generalization of these methods are proposed and their convergence properties are studied.
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 Gaussian Elimination The goal of forward elimination is to transform the coefficient matrix into an upper triangular matrix
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 Gauss-Jordan Elimination To solve a system, we use a technique called Gauss-Jordan elimination. We can use this technique to determine if the system has a unique solution, infinite solutions, or no solution.
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 Solving the Eigenvalue Problems In many cases of importance a finite difference approximation to the eigenvalue problem of a second-order differential equation reduces the problem to that of solving the eigenvalue problem of a tridiagonal matrix having the Sturm property.
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 Eigenvalues For large values of n, polynomial equations like this one are difficult and time-consuming to solve. Moreover, numerical techniques for approximating roots of polynomial equations of high degree are sensitive to rounding errors.
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 Completely Randomized Design Suppose we have 4 different diets which we want to compare. The diets are labeled Diet A, Diet B, Diet C, and Diet D. We are interested in how the diets affect the coagulation rates of rabbits. The coagulation rate is the time in seconds that it takes for a cut to stop bleeding.
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 Chi-Square When an analyst attempts to fit a statistical model to observed data, he or she may wonder how well the model actually reflects the data. How "close" are the observed values to those which would be expected under
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