Recent content by rbpl

  1. R

    Financial Model Backtesting and Regression Analysis?

    Hello everyone, I have a homework assignment in my financial mathematics class and I don't fully understand it, so here is my problem: I am supposed to backtest a given data set to see if a financial model works, in particular, for 30 maturity dates of the treasuries (bonds) I had to see how...
  2. R

    Game Theory a problem which is a bit similar to the Impossible Puzzle

    Thank you guys for your help. Mistermath that totally makes sense, when I was trying to see the pattern in the results for x^2 + y^2 I made a stupid miscalculation and for every 1^2 * 10^2... and 10^2 * 1^2... I wrote 100... instead of 101... which made other numbres just as attractive as...
  3. R

    Game Theory a problem which is a bit similar to the Impossible Puzzle

    There are 100 combinations for X + Y and 100 combinations for X^2 + Y^2. Since U and V could be any of the results we can assume that the correct solution is one of the 100 combination for 100 combinations. Whatever the result is for X + Y the guy has to check numbers for at least 1 result...
  4. R

    Game Theory a problem which is a bit similar to the Impossible Puzzle

    Game Theory a problem which is a bit similar to the "Impossible Puzzle" From numbers 1 to 10, two integers X, and Y (not necessarily distinct) are chosen by a referee . The referee informs secretly to Joe the integer U where U = X + Y . The referee informs secretly to Bob the integer V where V...
  5. R

    Riemann integrable sequences of functions

    Let f_n : [0,1] → [0,1] be a sequence of Riemann integrable functions, and f : [0, 1] → [0, 1] be a function so that for each k there is N_k so that supremum_(1/k<x≤1) of |f_n(x) − f(x)| < 1/k , for n ≥ N_k . Prove that f is Riemann integrable and ∫ f(x) dx = lim_n→∞ ∫ f_n(x) dx I am really...
  6. R

    Power Series Differentiation

    Is this kind of manipulations permissible: f'(x)=(n=1 to infinity)∑ (x^n-1)/(3^n) from this it follows that f'(x)=(n=1 to infinity)∑ (x^n-1)/(3^n-1+1) f'(x)=(n=1 to infinity)∑ (1/3)*((x/3)^(n-1)) f'(x)=(n=0 to infinity)∑ (1/3)*(x/3)^(n) If it is then I'm not sure if I see anything special here...
  7. R

    Power Series Differentiation

    Thank you for the quick response. So we have that: f'(x)=(n=1 to infinity)∑ (x^n-1)/(3^n) from this it follows that f'(x)=(n=0 to infinity)∑ (x^n-1)/(3^n-1) f'(x)=(n=0 to infinity)∑ (x/3)^(n-1) f'(x)=(n=1 to infinity)∑ (x/3)^(n) I got confused with limits of the summation am I correct? When...
  8. R

    Power Series Differentiation

    Consider the power series (n=1 to infinity) \Sigma (x^n)/(n*3^n). (a) Find the radius of convergence for this series. (b) For which values of x does the series converge? (include the discussion of the end points). (c) If f(x) denotes the sum of the series, find f'(x) as explicitly as...
  9. R

    Linear algebra: Jordan normal forms

    Suppose the characteristic polynomial of a matrix A is \lambda^3(\lambda-1)(\lambda-2). If the nullity of A is two, what are the possible Jordan normal forms of A up to conjugation?I think that an example of a matrix with such characteristic polynomial is: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1...
  10. R

    Linear Algebra, Inner Product of Matrices

    Thank you for your help.
  11. R

    Linear Algebra, Inner Product of Matrices

    Yes, I understand it makes sense now. So, I guess that in my w2 in the post where I used Gram-Schmidt, I schould have done this: (1 0) - (-1 0) (-3 1)(-1 0) (0 0) (1 0) . (-3 1) = ------------- (0 0) (-3 1)(-3 1) (0 0) (0 0) (-1 0) - (3/11) . (-3 1) = (1 0)...
  12. R

    Linear Algebra, Inner Product of Matrices

    Since S= (a b) such that a + 3b - c = 0 (c d) We have that S= (-3b-c b) (c d) Thus the basis for the Gram-Schmidt Orthogonalization is: (-3 1),(-1 0),(0 0) (0 0) (1 0) (1 0) This gives us: w1= (-3 1) (0 0) w2= (-1/10 -3/10) (1 0) w3= (1/2 0)...
  13. R

    Linear Algebra, Inner Product of Matrices

    let u=(a1 b1), v=(a2 b2), w=(a3 b3) (c1 d1) (c2 d2) (c3 d3) (a1 b1) . (a2 b2) = a1a2 + 2b1b2 + c1c2 + 2d1d2 (c1 d1) (c2 d2) There are four properties that: 1. <u,v>=<v,u> (a1 b1) . (a2 b2) = a1a2 + 2b1b2 + c1c2 + 2d1d2 (c1 d1) (c2 d2) (a2 b2) . (a1 b1) =...
  14. R

    Linear Algebra, Inner Product of Matrices

    Let M_2x2 denote the space of 2x2 matrices with real coeffcients. Show that (a1 b1) . (a2 b2) (c1 d1) (c2 d2) = a1a2 + 2b1b2 + c1c2 + 2d1d2 defines an inner product on M_2x2. Find an orthogonal basis of the subspace S = (a b) such that a + 3b - c = 0 (c d) of M_2x2...
  15. R

    Series Convergence/Divergence and Comparison Test

    I was trying to follow an example from my old calculus book the example was: lim x^x goes to lim(x^x)=lim(xlnx)=lim(lnx/x^-1)=lim(x^-1/-x^-2)=lim(-x)=0 So I tried to apply it there
Back
Top