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  1. M

    Cesaro mean question

    Thank you!!!!!!!
  2. M

    Cesaro mean question

    I have an=1/(10n), for n≠10k bn=log(n) if n=10k I think the argument should go as follows. Since b10 =1, b100=2, b1000= 3, etc., then, σn≤(1/n)[Ʃ10-n] +n*10-n Taking the limit of that as n→∞ would be zero. Does that make sense?
  3. M

    Cesaro mean question

    I think we have found a couple that will work, the difficult part is proving it. How do I do that?
  4. M

    Cesaro mean question

    What I have for the sequence I described is: σ10=.599 σ100=.101 σ1000=.032 But I'm not sure how to describe this formally.
  5. M

    Cesaro mean question

    I have a piecewise sequence for xn, where xn = √n for x10n , 1/n2 otherwise. I know that the series 1/n2 converges, so that part of the mean will go to zero when it is divided by n. For the other part, √n: at n=10, xn/n=.31 at n=100, xn/n=.1 at n=1000, xn/n=.031 I think that will...
  6. 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...
  7. M

    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...
  8. M

    Joint distribution of functions

    So 0\leqY1\leq2. The line will have a slope of -1, cutting the square diagonally. It will cut the square in half at t=1. What do I do with this information to get f(y)? F(y)=\intf(y), so I need to find an equation for the area, and differentiate. This will have two parts. First...
  9. M

    Joint distribution of functions

    You had me until you said to draw the line x1+x2=t. What value of do I use t?
  10. M

    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...
  11. M

    Joint density function

    Could somebody explain this in English?
  12. 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...
  13. M

    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...
  14. 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...
  15. M

    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...
  16. M

    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...
  17. M

    Orthogonal compliment proof

    If addition or scalar multiplication are redefined, then the zero vector can have nonzero entries. So since the problem doesn't say anything about that, I am to assume that everything is normal?
  18. M

    Orthogonal compliment proof

    For a row vector x dotted with the column vector ai, the resuting value will be the ith column of the 1xn zero vector. This for me does not guarantee that the value will be zero, however.
  19. M

    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...
  20. M

    Eigenvalue Problem

    (A+rI)x=(\lambda+r)x (A+rI)x-(\lambda+r)x=0 (A+rI-\lambdaI-rI)x=0 (A-\lambdaI)x=0 So the eigenvectors of A and A+rI are the same, right?
  21. M

    Eigenvalue Proof

    So if I prove those two determinants are equal, it necessarily follows that the two matricies have the same eigenvalues and algebraic multiplicities, because the characteristic polynomials are the same?
  22. M

    Eigenvalue Problem

    I don't see why I should be assuming that \lambda in the first equation should be equal to \lambda in the second equation. The same goes for x. It's really giving me trouble as I work with this.
  23. M

    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?
  24. M

    Eigenvalue Problem

    [/B][/B] The eigenvectors are the solution to: (A-(\lambda-r)I)x=0 What do you suppose is meant by "compare the eigenvectors and eigenvalues?"
  25. 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...
  26. M

    Determinant proof

    det((C^-1)AC)=det(C^-1)*det(A)*det(C)=(1/det(C))*det(C)*det(A)=(det(C)/det(C))*det(A)=det(A). Is that it?
  27. M

    Matrix problem

    How embarrassing.
  28. M

    Dimension problem

    I understand why W would equal V. Every linear combination of vectors in W is in W, and since W and V have the same number of elements in a basis, and W is in V, then W=V. I just don't know how to illustrate that.
  29. M

    Matrix problem

    (A+A^T)is symmetric, (A-A^T)is skew symmetric, but adding them together produces 2A, not A. I'm not sure what to do with this information.
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