Recent content by mlarson9000

  1. M

    Can the Cesaro Mean Be Zero Even if the Sequence Diverges?

    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?
  2. M

    Can the Cesaro Mean Be Zero Even if the Sequence Diverges?

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

    Can the Cesaro Mean Be Zero Even if the Sequence Diverges?

    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.
  4. M

    Can the Cesaro Mean Be Zero Even if the Sequence Diverges?

    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...
  5. M

    Can the Cesaro Mean Be Zero Even if the Sequence Diverges?

    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...
  6. 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...
  7. 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?
  8. 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...
  9. M

    Finding the Joint and Density Functions for Independent Uniform Random Variables

    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...
  10. 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...
  11. M

    How can suppose, let, and consider be used in proof writing?

    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...
  12. M

    Proving Orthogonal Compliments of Subspaces in Matrix Algebra

    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?
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