Recent content by jacobi1

I don't quite understand you. Are you simply trying to say that one vector of observations does not equal another? In that case, it would be $$(\mu_{Aa_1},\mu_{Aa_2},\mu_{Aa_3}...) \neq (\mu_{AA_1}...) \neq ...$$ Can you elaborate a little more on what you need? Also, to type $\LaTeX$, use \$...

Hint: $\frac{\ln(t^2)}{t}= 2 \frac{\ln(t)}{t}$. The rest of your evaluation is correct.

It looks right. I don't exactly know what the problem is. All I can suggest is that you put a more explicit path to the image in the \includegraphics command (i.e. \includegraphics{c: \folder\folder2\...\shm\ask2.jpg}) and remove the \graphicspath command in the preamble. Maybe that will help...

Four things. 1) Did you type \includegraphics{ask2} in the preamble? You can't insert images in the preamble. 2) You have to put the file extension after the name. If it is a .png, then write \includegraphics{ask2.png}. 3) If you put the picture in the same folder as the source files, you don't...

Hello and welcome to MHB, labrat! It seems to me that the coefficients of your 4th order polynomial are off. The area you get with your 5th order polynomial makes more sense than the one you get with the 4th order approximation. I can't find any problems with the way you calculated your...

Another, purely analytic, way of looking at it:

Congratulations, Opalg, your answer is correct. And much faster than mine, too.:) I did this the hard way. As in, the long, stupid way.

(Swearing)(Swearing)(Swearing) I can't believe I made such a stupid mistake. Forgetting to substitute $k-1$ for $k$...:mad: Anyway, if you iterate CORRECTLY k times, you get $$ g(k) = 2^k g(0) + \sum_{j=0}^{k} 2^j 2^{2^{k-j}}.$$ Then, $$ f(n) = f(2) \log_{2} n + \sum_{j=0}^{\log_{2} \log_{2}...

Oh, I see. Since $$ g(k) = 2 g(k-1) +2^{2^k}, $$ $$ g(k-1) = 2 g(k-2) + 2^{2^k}. $$ Substituting into the previous relation, we have that $$ g(k) = 2 \left ( 2 g(k-2) +2^{2^k} \right ) +2^{2^k} = 4 g(k-2) + 2 \times 2^{2^k} + 2^{2^k} = 4 g(k-2) +3 \times 2^{2^k}. $$ Iterating c times, the...

I include the probability that it may have visited Q previously.

The Wronskian of two functions $ f_1$ and $ f_2$ is defined as \[ W (f_1, f_2 ) = \left | {\begin{array}{cc} f_1 & f_2 \\ f_{1}^{'} & f_{2}^{'} \\ \end{array} } \right | \] Using this definition, what then is the Wronskian determinant? Then, if the determinant is never 0 on the interval, the...

The image shows a network of rooms. A ball starts in room P. If the ball moves from one room to another adjacent one every second (assume no time is spent between the rooms) and it randomly chooses a room to go to, find the probability that it reaches room Q after n seconds. A room is adjacent...

Your initial condition would probably have to be in terms of T(n), not S(n). You can find T(0)= -1 and T(1) = -1 from the equation, though. If you use the method from my post in http://mathhelpboards.com/discrete-mathematics-set-theory-logic-15/solve-f-n-2f-sqrt-n-n-14405.html, you can find...

While all the other conditions of Case 3 of the Master Theorem hold, I don’t believe that the regularity condition, $$ 2 \times 2^{k/2} \leq d \times 2^k, \ d < 1, \ k > N, $$ holds. This holds for $ k \geq 2 \left (1-\log_{2} d \right ) $, but I don’t know…I’d like to have a numerical value...