Thank you, so I can write:
let x_m be the x value at the absolute minimum;
for x_p ≥ x_m and for x ≥ x_p; dy/dx ≥ 0, hence y_b ≥ y_p as x_b ≥ x_p;
for x_p ≤ x_m and for x ≤ x_p; dy/dx ≤ 0, hence y_a ≥ y_p as x_a ≤ x_p;
I think these two cover everything and I don't necessarily need a 3rd...
Summary: Given three points on a positive definite quadratic line, I need to prove that the middle point is never higher than at least one of the other two.
I am struggling to write a proof down for something. It's obvious when looking at it graphically, but I don't know how to write the...
I have a vector B of length N, I would like to prove that:
∑n=0 to N-1 (|Bn|x) ≥ Nαx
where:
x > 1;
α = (1/N) * ∑n=0 to N-1 (|Bn|) (i.e., The mean of the absolute elements of B).
and ∑n=0 to N-1 (||Bn|-α|) ≠ 0; (i.e., The absolute elements of B are not all identical).
I believe the above to...
Hi Scott! Thanks for these ideas. I really like the last one, though unfortunately the centers do not necessarily form a convex polygon. However, on reconsidering the problem I am dealing with, I would not be interested in points that contributed to a non-convex shape, so I think all I might...
I am trying to find the most efficient way to select points on a 2d plane from a set that maximizes the area of the of the shape they define when joined together.
The points are all paired (sharing the same A->B vector), with these pairs also appearing mirrored about the origin. Here is an...
Thankyou for your response!
Your proposed method would work perfectly if the list of vectors had a fixed, pre-determined order in which they were fed into your algorithm. If I understand correctly you suggest to take the first two vectors, \vec{a} and \vec{b}, find the maximum dot product by...
Thanks for the reply maajdl,
I altered the coordinates in this way as you suggested before and I didn't feel any closer to a solution, the integrand became a massive long mess and I couldn't simplify it. If I find my notes I will post it up (took me a while to re-arrange it).
I think for...
Wasn't sure whether to post this in the computing section or not but here goes anyway,
I have n number of 2d vectors (all have the same magnitude),
for each vector I can choose whether or not to multiply it by -1 (spinning it through 180 degrees),
all of the vectors are then added together,
The...
Here is the beast
\iint_{(ax+\mu _{1})^{2}+(bx+cy+\mu _{2})^{2}\leqslant z}\frac{1}{2\pi \sigma ^{2}}e^{-(\frac{1}{2\sigma ^{2}})(x^{2}+y^{2})}dxdy
The integral gives the C.D.F. of (ax+\mu _{1})^{2}+(bx+cy+\mu _{2})^{2}\leqslant z where x and y are identically distributed gaussian random...
Thanks for the reply. I did actually reply last night but the post seems to have disappeared... Anyway, I looked up the characteristic function of the non-central chi-squared distribution as you suggested. When multiplying these characteristic functions together they simplify to the exact same...
Hi,
I am struggling trying to find the (equation of the) pdf of the sum of (what I believe to be) two non-central chi-squared random variables.
The formula given on wikipedia (http://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution) shows that the random variable associated with...