Hmm. Alright then by Cauchy-Schwartz I can say,
$$(\sum_{i=1}^{n} x_i \times 1)^2 \le (\sum_{i=1}^{n}x_i^2) (\sum_{i=1}^{n}1) = n\sum_{i=1}^{n}x_i^2 < n^2 \sum_{i=1}^{n}x_i^2$$
Which was what I wanted.
Thanks!
Yes I am, but I'm not sure how to use it here. If I was interested in both a x_i and y_i then I would see how to use it here, but here I'm only looking at a x_i.
$$\sum_{i=1}^{n} x_i^2 > \frac{1}{n^2}(\sum_{i=1}^{n} x_i)^2$$
Note: each x_i is any observation (or statistic) it can be any real number and need not be constrained in anyway whatsoever, though you can take n > 1 and integer (i.e. there is at least two observations and the number of...
Would you mind briefly mentioning the outline for the proof (i) => (ii) for rational c? Is it simply because the sum of two rational numbers always yields a rational number.
Yeah that is way above the level I was hoping for. I found an example where (2) holds but (1) doesn't online. The source...
The two properties every linear transformation T: V -> W has to satisfy is
T(u + v) = T(u) + T(v), for u,v in V (i)
T(cu) = cT(u) for u in V and scalar c (ii)
I'm trying to find a transformation which satisfies (i) but doesn't satisfy (ii) [I've been able to find the opposite for what it's...
Thanks for the suggestion! The field I'll probably be working with is more-so mathematics/economics (finance) than actual science.
The same methods probably apply in a non-scientific setting. Would general chemistry and standard physics I & II sequence be enough background for the scientific...
An introductory text is preferable. Topics relevant (not a deal-breaker if not covered): Poisson process, Markov chains, renewal theory, models for queuing, and reliability.
Also, in the future I'd like to dabble in stochastic calculus, but my background in measure theory is non-existent. I've...
The same thing happens. Since D<0 you have a saddle point, in some directions you have local maxes and in others you have local mins. That is when D<0 you don't even bother to check the sign of fxx because D<0 => saddle point. The example I chose was meant to be illustrative of where the name...
It's the sign of D that matters not fxx,fyy, or fxy individually.
If D < 0 that is fxxfyy < (fxy)^2 you have a saddle point.
For an example, consdier f(x,y) = x^2 - y^2, a hyperbolic paraboloid (or more informally a saddle). Think of it as a pringle chip.
Find the critical points
fx = 2x =...
Yep it is possible, this is a paper I came across some time ago when looking for the same answer.
http://www.sefi.be/conference-2012/Papers/Papers/030.pdf
Starts talking about higher order partial derivatives at bottom of page 3. It's a clever use of the product rule.
Conditions for calculating flux integrals? [Figured it out]
If one uses Stokes' theorem and if two oriented surfaces S1 and S2 share a boundary ∂s then the flux integral of curl(F) across S1 equals the flux integral of curl(F) across S2. However, in general it won't be true that flux integral G...
Homework Statement
You toss a fair die 4 times. You let the random variable X denote the number of times a toss results in 1 or 2, and Y denote the number of time a toss results in 3,4, or 5.
a) Find P(X = 1, Y = 2)
b) Find P(X = Y)Homework Equations
None that I know of.The Attempt at a...
Yes. That would be logically true, if you buy that row operations preserve linear relations between columns but not rows. You wouldn't even need to invent column operations you can instead claim the original proposition for the transpose of a matrix.
That still doesn't explain why it is true.