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Problem 10.7. Show that azn-e* has n roots with Izl < 1 if lal > e....
Olomorphic. f F has a maximum value on U, then f is constant. One proof follows a line of reasoni...
Task 204！
olomorphic. f F has a maximum value on U, then f is constant. One proof follows a line of reasoning that is typical for analytic functions, by which information nea one point can be transferred to other points by moving along a contour. Suppose Ifl has a maximun value at zo. Then the local version of the maximum modulus principle implies that f must be constan near zo. Consequently, the Taylor series of f at any point near...
Here you are asked to prove the Fundamental Theorem of Algebra a different way by using Rouché's Theorem. Where n E N, consider the polynomial n-1 Pn (z)z" k-0 Using the circular contour C-[z...
Here you are asked to prove the Fundamental Theorem of Algebra a different way by using Rouché's Theorem. Where n E N, consider the polynomial n-1 Pn (z)z" k-0 Using the circular contour C-[z : zR with R appropriately chosen, (a) prove that pn(2) has (counting multiplicity) precisely n zeros in the open disc D(0, R); (b) also show that Pn(z) has no zeros in C \ D(0, R)
Here you are asked to prove the Fundamental Theorem of Algebra...
Problem 4 Let x(t) be a continuous time signal whose Fourier transform has the property that Xe(ja)0 for lal 2 2,00...
Problem 4 Let x(t) be a continuous time signal whose Fourier transform has the property that Xe(ja)0 for lal 2 2,000. A discrete time signal aIn]x(n(0.5x 10-3)) is obtained. For each of the following constra ints on Xa(e/n), the Fourier transform of xaln], determine the coresponding constraint on Xe(ja) a) X(en) is real b) The maximum value of X4 (ea) over all is 1 c) Xa(ea)= Xa(e/ a-)
Problem 4 Let x(t) be a continuous time signal whose Fourier transform...
1. Assume a consumer has as preference relation represented by u(c1, 2) for g E (0,...
1. Assume a consumer has as preference relation represented by u(c1, 2) for g E (0, 1) and oo > n > 2, with x E C = Ri. Answer thefollow (x1+x2)" ing: a. Show the preference relation that this utility function induces "upper b. Show the preference relation these preferences represent are strictly C. Give another utility function that generates exactly the same behavior as level sets that are convexif U(x) is Convex for any xeX monotonic. this one....
Problem 1: The matrix e^A is defined by the Mclaurin series e^A=1+A/1!+A^2/2!+A^3/3!+........+A^n/n! This computation ca...
Problem 1:
The matrix e^A is defined by the Mclaurin series
e^A=1+A/1!+A^2/2!+A^3/3!+........+A^n/n!
This computation can be quite difficult, as this problem
illustrates.
a)Enter the function
function E=matexp(A)
E=zeros(size(A));
F=eye(size(A));
k=1;
while norm (E+F-E,1) > 0
E=E+F;
F=A*F/k;
k=k+a;
end
that estimates e^A using Mclaurin series.
b)Apply matexp to the matrix a=[99 -100; 137 -138] to obtaion
matrix A_Mclaurin
c)A_Mclaurin is far from the correct result.ompute the true
value of e^A using the MATLAB function expm as follows:
>>showdemo expmdemo
The...
Fill all Answer Blanks and show all calculations in a separate sheet of paper. Problem: Given...
Fill all Answer Blanks and show all calculations in a separate sheet of paper. Problem: Given the Pole-Zero Plot (one pole and one zero at the origin) of a causal filter with a normalized magnitude frequency response (max |H(w)l 1): 0.8 a) It is a FIR or IIR filter? b) what is the R.O.C of the filter ? c) Is the filter stable BIBO? Answer: Answer: Izl> Arıswer: d) The magnitude frequency response has a maximum peak at w0. Answer:...
Problem 4 Suppose X1, ..., Xn ~ f(x) independently. Let u = E(Xi) and o2 = Var(Xi). Let X Xi/n. (1) Calculate E(X) and...
Problem 4 Suppose X1, ..., Xn ~ f(x) independently. Let u = E(Xi) and o2 = Var(Xi). Let X Xi/n. (1) Calculate E(X) and Var(X) (2) Explain that X -> u as n -> co. What is the shape of the density of X? (3) Let XiBernoulli(p), calculate u and a2 in terms of p. (4) Continue from (3), explain that X is the frequency of heads. Calculate E(X) and Var(X). Explain that X -> p. What is the shape...
5. Let Xi,..., X, be iid N(e, 1). (a) Show that X is a complete sufficient statistic. (b) Show th...
1.(c)
2.(a),(b)
5. Let Xi,..., X, be iid N(e, 1). (a) Show that X is a complete sufficient statistic. (b) Show that the UMVUE of θ 2 is X2-1/n x"-'e-x/θ , x > 0.0 > 0 6. Let Xi, ,Xn be i.i.d. gamma(α,6) where α > l is known. ( f(x) Γ(α)θα (a) Show that Σ X, is complete and sufficient for θ (b) Find ElI/X] (c) Find the UMVUE of 1/0 -e λ , X > 0 2) (x...
Please show the solutions for all 4 parts! Problem 1 Let m E Z that is...
Please show the solutions for all 4 parts!
Problem 1 Let m E Z that is not the square of an integer (ie. mメ0, 1.4.9, ). Let α-Vm (so you have a失Q as mentioned above) (i) Prove the following:Qla aba: a,b Q is a subring of C, Za]a +ba: a, b E Z is a subring of Qla], and the fraction field of Z[a] is Q[a]. (3pts) (ii) Prove that Z[x]/(X2-m) Z[a] and Qx/(x2 mQ[a]. (3pts) i Let n be...
2. (5 pts) Assume A E Rm** with m > n has (full) rank n. Show that At = (ATA)TAT, What is the pse...
2. (5 pts) Assume A E Rm** with m > n has (full) rank n. Show that At = (ATA)TAT, What is the pseudo-inverse of a vector u R" regarded as an m x 1 matrix? 3. (5 pts) Let B AT where A is the matrix in Problem 1. Use Matlab to find the singular value decomposition and the Moore-Penrose pseudo-inverse of B. Then solve minimum-norm least squares problem minl-ll : FE R minimizes IBr-ey where c- [1,2. Compare...
Task 204！
olomorphic. f F has a maximum value on U, then f is constant. One proof follows a line of reasoning that is typical for analytic functions, by which information nea one point can be transferred to other points by moving along a contour. Suppose Ifl has a maximun value at zo. Then the local version of the maximum modulus principle implies that f must be constan near zo. Consequently, the Taylor series of f at any point near...
Here you are asked to prove the Fundamental Theorem of Algebra a different way by using Rouché's Theorem. Where n E N, consider the polynomial n-1 Pn (z)z" k-0 Using the circular contour C-[z : zR with R appropriately chosen, (a) prove that pn(2) has (counting multiplicity) precisely n zeros in the open disc D(0, R); (b) also show that Pn(z) has no zeros in C \ D(0, R)
Here you are asked to prove the Fundamental Theorem of Algebra...
Problem 4 Let x(t) be a continuous time signal whose Fourier transform has the property that Xe(ja)0 for lal 2 2,000. A discrete time signal aIn]x(n(0.5x 10-3)) is obtained. For each of the following constra ints on Xa(e/n), the Fourier transform of xaln], determine the coresponding constraint on Xe(ja) a) X(en) is real b) The maximum value of X4 (ea) over all is 1 c) Xa(ea)= Xa(e/ a-)
Problem 4 Let x(t) be a continuous time signal whose Fourier transform...
1. Assume a consumer has as preference relation represented by u(c1, 2) for g E (0, 1) and oo > n > 2, with x E C = Ri. Answer thefollow (x1+x2)" ing: a. Show the preference relation that this utility function induces "upper b. Show the preference relation these preferences represent are strictly C. Give another utility function that generates exactly the same behavior as level sets that are convexif U(x) is Convex for any xeX monotonic. this one....
Problem 1:
The matrix e^A is defined by the Mclaurin series
e^A=1+A/1!+A^2/2!+A^3/3!+........+A^n/n!
This computation can be quite difficult, as this problem
illustrates.
a)Enter the function
function E=matexp(A)
E=zeros(size(A));
F=eye(size(A));
k=1;
while norm (E+F-E,1) > 0
E=E+F;
F=A*F/k;
k=k+a;
end
that estimates e^A using Mclaurin series.
b)Apply matexp to the matrix a=[99 -100; 137 -138] to obtaion
matrix A_Mclaurin
c)A_Mclaurin is far from the correct result.ompute the true
value of e^A using the MATLAB function expm as follows:
>>showdemo expmdemo
The...
Fill all Answer Blanks and show all calculations in a separate sheet of paper. Problem: Given the Pole-Zero Plot (one pole and one zero at the origin) of a causal filter with a normalized magnitude frequency response (max |H(w)l 1): 0.8 a) It is a FIR or IIR filter? b) what is the R.O.C of the filter ? c) Is the filter stable BIBO? Answer: Answer: Izl> Arıswer: d) The magnitude frequency response has a maximum peak at w0. Answer:...
Problem 4 Suppose X1, ..., Xn ~ f(x) independently. Let u = E(Xi) and o2 = Var(Xi). Let X Xi/n. (1) Calculate E(X) and Var(X) (2) Explain that X -> u as n -> co. What is the shape of the density of X? (3) Let XiBernoulli(p), calculate u and a2 in terms of p. (4) Continue from (3), explain that X is the frequency of heads. Calculate E(X) and Var(X). Explain that X -> p. What is the shape...
1.(c)
2.(a),(b)
5. Let Xi,..., X, be iid N(e, 1). (a) Show that X is a complete sufficient statistic. (b) Show that the UMVUE of θ 2 is X2-1/n x"-'e-x/θ , x > 0.0 > 0 6. Let Xi, ,Xn be i.i.d. gamma(α,6) where α > l is known. ( f(x) Γ(α)θα (a) Show that Σ X, is complete and sufficient for θ (b) Find ElI/X] (c) Find the UMVUE of 1/0 -e λ , X > 0 2) (x...
Please show the solutions for all 4 parts!
Problem 1 Let m E Z that is not the square of an integer (ie. mメ0, 1.4.9, ). Let α-Vm (so you have a失Q as mentioned above) (i) Prove the following:Qla aba: a,b Q is a subring of C, Za]a +ba: a, b E Z is a subring of Qla], and the fraction field of Z[a] is Q[a]. (3pts) (ii) Prove that Z[x]/(X2-m) Z[a] and Qx/(x2 mQ[a]. (3pts) i Let n be...
2. (5 pts) Assume A E Rm** with m > n has (full) rank n. Show that At = (ATA)TAT, What is the pseudo-inverse of a vector u R" regarded as an m x 1 matrix? 3. (5 pts) Let B AT where A is the matrix in Problem 1. Use Matlab to find the singular value decomposition and the Moore-Penrose pseudo-inverse of B. Then solve minimum-norm least squares problem minl-ll : FE R minimizes IBr-ey where c- [1,2. Compare...
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