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...
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...
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...
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...
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...
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...
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...
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...
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...
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)...
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)...
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...
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