Let P X X 3 X 1 And Q X X 2 X Perform Long Division Of P By Q In The Following F

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Let p(x) = x 3 + x + 1, and q(x) = x 2 + x. Perform long division of p, by q, in the following fields. (I.e. write p(x) = f(x)q(x) + r(x) where degr < degq.) (a) F = R (b) F = Z3 (Hint: Use (a).) (c) F = Z5 (Hint: Use (a).)

 
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Let P2 Denote The Vector Space Of All Polynomials With Real Coefcients And Of De

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Please help me solve this problem. Thanks. I have attached the image of the question here.

2. Let P2 denote the vector space of all polynomials with real coefficients and of degree at most 2. Define a function T : P2 —&gt; P; by d2 dT(p(w)) — wwflw) + Qfiflw), for all p(m) E P2. In addition, let 5′ = (1, m, .132) be the standard basis of P2. (a) Show that T : P2 —&gt; P2 is a linear operator.(b) Find the matrix A for which [T(p(3:))]3 = A [p(:1:)]3 for all 19(37) E P2.

 
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Let P4 Be The Set Of All Polynomials With The Degree At Most 4 I P4 Contains All

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Let P4 be the set of all polynomials with the degree at most 4, i.e., P4 contains all polynomials of the formp(x) = a4x4 + a3x3 + a2x2 + a1x + a0.- Show that P4 is a vector space.

Let P4 be the set of all polynomials with the degree at most 4, i.e., P4 contains all polynomials of the formp(x) = a4x4 + a3x3 + a2x2 + a1x + a0. ANSWER : , where

 
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Let P 1 P 400 Be A Sample Computed By P X Y 2 Z 3 W 4 Where X 1 X 2 X 400 Y 1 Y

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P = X + Y^2 + Z^3 + W^4, where

X_1, X_2, .., X_400Y_1, Y_2, .., Y_400Z_1, Z_2, .., Z_400W_1, W_2, .., W_400

are samples from Uniform(0,1) distribution. Find 90% confidence interval for the variance of P. Note: Use at least fifty thousand simulated samples to generate sampling distr. for the variance of P.

 
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Let Pr Be The N X N Matrix Whose Entries Are All Ones Except For Zeros Directly

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I need help with linear algebra help for this question number 17

17. Let Pr be the n x n matrix whose entries are all ones.except for zeros directly below the main diagonal; forexample.1 1 10 111Ps =1HOH1HPPH0 1HOH1Find the determinant of Pr.

 
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Let Pt Be A Random Walk With Increment E T And Let E T Be I Normal With Mean U A

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Let Pt be a random walk with increment Et, and let Et be i.i.d. normal with mean u and variance sigma2. Assume t0 = 1.

1. Derive the unconditional mean and variance of Pt.

2. Derive the conditional mean and variance of Pt given a value of Pt-1 = x.

3. Compare and contrast the behavior of the unconditional and conditional variance, as t –infinity .

 
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Let Q Be A Symmetric Transition Probability Matrix That Is 53 Q For All I

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Let Q be a symmetric transition probability matrix, that is qy qu for all i,j- 1,… ,N. Consider a Markov chain which, when the present state is i, generates the value of a random variable X such that P(X j) dy, and if X-j, then either moves to state j with probability b,/(b, + bi), or remains in state i otherwise, where b,, j-1,…, N, are specified positive numbers. Show that the resulting Markov chain is time reversible with stationary probabilities a Cb,, j1,.., N

2. Let Q be a symmetric transition probability matrix, that is, 53,- }- = q},- for alli, j. Consider a Markov chain which, when the present state is i, generatesthe value of a raindom variable X such that P{X = j} = (3,}, and if X = j,then either moves to state j with probability b}- /(b,- + bf), or remains in state1′ otherwise, where b}, j = l . . . , N, are specified positive numbers. Show that the resulting Markov chain is time reversible with limiting probabilities

 
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Let R Be The Region Bounded By The Graphs Of Y Sin Pie Times X And Y X 3 4x A

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let R be the region bounded by the graphs of y = sin(pie times x) and y = x^3 – 4x.a) find the area of Rb) the horizontal line y = -2 splits the region R into parts. write but do not evaluate an integral expression for the area of the part of R that is below this horizontal line.c) The region R is the base of a solid. For this solid, each cross section perpendicular to x-axis is a square. Find the volume of this solid. d) the region R models the surface of a small pond. At all points in R at a distance x from the y-axis, the depth of the water is given by h(x)=3-x. find the volume of the water in the pound.

 
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Let Random Variables X And Y Respectively Denote The Number Of Heads And Tails O

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Let random variables X and Y respectively denote the number of heads and tails obtained in a sequence of n independent flips of a fair coin.

(a) What kind of discrete random variable is X? Specify its range, PMF values,mean and standard deviation.

(b) Let D = X−Y denote the difference between the number of heads and tails. Usingthe central limit theorem, find a suitable approximation for the probabilitythat |D| > m, where m is a positive integer m.

(c) Evaluate this probability for the following special situation involving a very large number of flips: n = 1020 and m = 109(i.e. the difference between the number of heads and tails exceeds one billion!)

Binomial approximation using central limit theorem1 Subject : Probability and StatisticsAssignment Title: Binomial approximation using central limit theoremCompilation Date: 17Th December 2015…

 
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Let Re Q Be The Subring Consisting Of Polynomials Dot A12t And Such That Do Ei G

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Prove that the ring R is not Noetherian. Prove that the ring R is not Noetherian. Prove that the ring R is not Noetherian. Prove that the ring R is not Noetherian.

5 . Let RE Q` be the subring consisting of polynomials } = dot a12t . .. + and`&quot;such that do EI . Given a subgroup A in O ( viewed as an abelian group viaaddition ) , consider the subset I CR consisting of polynomials ajax t … + and`such that aj EA.

 
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