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?
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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?
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.
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...
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?
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.
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?
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...
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.