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  1. M

    Cesaro mean question

    Homework Statement Define the cesaro mean as σ=(1/n)(x1 +...+xn) Can it happen that xn >0 for all n, and limsup xn =∞, but limσ=0 Homework Equations The Attempt at a Solution I think I am supposed to construct a piecewise sequence, with ln(n), but I can't figure this out or the...
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    Poisson MLE and Limiting Distribution

    Homework Statement Let yi denote the number of times individual i buys tobacco in a given month. Suppose a random sample of N individuals is available, for which we observe values 0,1,2,... for yi. Let xi be an observed characterisitc of these individuals (for example, gender). If we...
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    Joint distribution of functions

    Homework Statement X1 and X2 are independent~u(0,1) Y1=X1+X2 Y2=X1-X2 Find the density function of Y1 Homework Equations X1=(Y1+Y2)/2 X2=(Y1-Y2)/2 0\leqY1\leq2 -1\leqY2\leq1 0\leqY1+Y2\leq2 0\leqY1-Y2\leq2 -y1\leqy2\leq2-y1 -1\leqy2\leqy1 The Attempt at a...
  4. M

    Joint density function

    Homework Statement Let X and Y be independent uniform (0,1) random variables. a. find th ejoint density of U=X, V=X+Y. b. compute the density funciton of V. Homework Equations The Attempt at a Solution Part a. is not a problem. I don't understand how the bounds for part b...
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    Multiple integral with substitution

    Homework Statement This is going to be confusing to read, as I don't know how to make this look right. The first integral is from 0 to L-2d, the second from x1+d to L-d, and the third from x2 to L. (F(x)=1) 1.) 0\intL-2d,x1+d\intL-d,x2+d\intL dx3dx2dx1 2.) 0\intL-2d,x1+d\intL-d...
  6. M

    Linear regression problem

    Homework Statement Evaluate the partial effect of age of a firm on growth.(evaluated at the means) Homework Equations Growth=\beta0+\beta1age+\beta2age^2+\beta3size*age+\beta4plant*age The Attempt at a Solution We're supposed to do something like this...
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    Basic proof writing question

    Homework Statement This isn't a homework problem, but I just had a general question about the language of writing proofs. I often see words like "suppose", "let", and "consider" in proofs. Could someone explain to me if there are rules to applying these? It doesn't seem like they are just...
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    Book recomendation for Econometrics class

    I need some help for my grad Econometrics class. The book we are using (Woolridge, Introductory Econometrics), doesn't go quite as deep into the math as the lecture does. As a result, it is difficult for me to follow what's going on, even if I read ahead. If anyone could recommend a text that...
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    Orthogonal compliment proof

    Homework Statement Let A be an mxn matrix. a. Prove that the set W of row vectors x in R^m such that xA=0 is a subspace of R^m. b. Prove that the subspace W in part a. and the column space of A are orthogonal compliments. Homework Equations The Attempt at a Solution a. to...
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    Eigenvalue Proof

    Homework Statement Prove that similar square matricies have the same eigenvalues with the same algebraic multiplicities. Homework Equations C^-1PC=Q The Attempt at a Solution Am I supposed to show that (P-\lambdaI)x=(C^-1PC-\lambdaI)x?
  11. M

    Eigenvalue Problem

    Homework Statement Let A be an nxn matrix and let I be the nxn identity matrix. Compare the eigenvectors and eigenvalues of A with those of A+rI for a scalar r. Homework Equations The Attempt at a Solution I think I should be doing something like this: det(A-\lambdaI), and...
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    Determinant proof

    Homework Statement If A and C are nxn matricies, with C invertible, prove that det(A)=det((C^-1)AC). Homework Equations The Attempt at a Solution I think the way to go is to show that if A=(C^-1)AC, then det(A)=det((C^-1)AC), but I'm not sure how to show A=(C^-1)AC. I know...
  13. M

    Subspace problem

    Homework Statement Let W1 and W2 be two subspaces of R^n. Prove that their intersection is also a subspace. Homework Equations The Attempt at a Solution I know that in R^2 and R^3 the intersection would be the origin, which would be the zero vector, which would be a subspace...
  14. M

    Matrix problem

    Homework Statement An nxn matrix C is skew symmetric if C^t = -C. Prove that every square matrix A can be written uniquely as A = B + C where B is symmetric and C is skew symmetric. Homework Equations The Attempt at a Solution No clue.
  15. M

    Dimension problem

    Homework Statement Prove that if W is a subspace of an n-dimensional vector space V and dim(W) = n, then W=V Homework Equations The Attempt at a Solution I don't know where to start.
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    Courses Math course advice sought

    I plan on studying math through real analysis. I am taking calc 3, and linear algebra at the moment. Calc 3 is not a problem for me, but linear algebra is by far the most difficult class I've had in my entire life. I'm still hoping I can get a B, but I may have blown that with the test I took...
  17. M

    Measure Theory

    Hi, I am pursuing graduate studies in economics, and I hear that "measure theory" is one of the classes that will impress admission commitees. I don't see anything by that name in my school's catalog. Does this class go by another name sometimes?
  18. M

    Another Linear Transformation problem

    Homework Statement Let F be the vector space of all functions mapping R into R, and letT:F-F be a linear transformationsuch that T(e^2x)=x^2, T(e^3x)= sinx, and T(1)= cos5x. Find the following, if it is determined by this data. Homework Equations a. T(e^5x) b. T(3+5e^3x) c. T(3e^4x)...
  19. M

    Linear Transformation Problem

    Homework Statement Let T: P3-P3 be the linear transformation defined by T(p(x))= D^2(p(x))-4D(p(x)) + p(x). Find the Matrix representation of A of T, where B = (x, 1+x, x+x^2, x^3). Homework Equations The Attempt at a Solution I don't know where to start here. What is D? Is...
  20. M

    Determining if set is a real vector space

    Homework Statement The set R^2 with addition defined by <x,y>+<a,b>=<x+a+1,y+b>, and scalar multiplication defined by r<x,y>= <rx+r-1,ry>. The answer in the back of the book says it is a vector space, but I am having trouble proving that 0+v=v and v+(-v)=0 Homework Equations The...
  21. M

    Determining if a set is a subspace

    Homework Statement Determine whether or not the set of all functions f such that f(1)+f(-1)=f(5) is a subspace of the vector space F of all functions mapping R into R. Homework Equations The Attempt at a Solution I think that (f(1)+f(-1))+(g(1)+g(-1))=(f+g)(1)+(f+g)(-1)=(f+g)(5)...
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