Rod Carvalho
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# 111 Comments

 Feb 19 comment Cleaning a signal and computing period @leonbloy: You're right. The solution I proposed is arguably ugly, but implementable using analog electronics. It's how digital signals are regenerated (if I remember my communication systems classes properly). Feb 19 comment Cleaning a signal and computing period @leonbloy: It's hard to implement a median filter using analog electronics, though. Oct 4 comment Prove $\forall x(C \land D) \equiv (\forall x C) \lor D$ Why the edit? $\equiv$ and $\Longleftrightarrow$ are not the same thing. Oct 1 comment Formula connecting x and y en.wikipedia.org/wiki/Drag_%28physics%29 Sep 30 comment Maximizing and minimizing Var(X) @Henry: Leaving the "easy and short" work to the OP is even easier and shorter. Unless I am paid by the word, which I am not, I will take the liberty of leaving some work to the OP. Sep 30 comment Is it possible for a scalar (or vector) field to be non-smooth? @Ryan: Is "made up of points that don't join up" an euphemism for "discontinuous"? Sep 30 comment Maximizing and minimizing Var(X) @BrianM.Scott: True. But I am lazy and felt like shortening the post. Sep 30 comment Is this a correct way to convert an convolution equation into differential/difference equation? @Tim: You can always obtain a 1st order ODE, but it may not be a scalar one. What I am alluding to is that any $n$-th order scalar ODE can be written as a 1st order vector ODE in $x \in \mathbb{R}^n$. I know this is not the answer you had in mind. Since I am an engineer, I view poles as elements that store energy (like capacitors or springs). Obtaining a 1st order scalar ODE is equivalent to saying that the impulse response can be replicated by a physical system with one single energy-storage element. This is a very restrictive requirement. Sep 27 comment Why does positive semi-definiteness in this inequality imply a convex set? Not quite. $x^T A x$ is convex only when matrix $A$ is positive definite / semidefinite. Sep 24 comment What is the difference between an array and a vector? @Killrawr: What is a graph of length $N$? Sep 24 comment I don't understand $\sqrt{-9i}$. @Thomas: So, could we say that there are two solutions, and that these two solutions can be represented in infinitely many ways in polar form? Sep 24 comment I don't understand $\sqrt{-9i}$. @Thomas: I suppose that the answer is that the angle in the polar representation must be restricted to $[0, 2 \pi]$ or $[-\pi, \pi]$, otherwise $z^2 + 1 = 0$, for example, has an infinite number of solutions. Sep 24 comment Summation of a finite series involving permutations. @Limitless: You're right. Sep 24 comment I don't understand $\sqrt{-9i}$. @Thomas: Then explain why $$\left(3 e^{i (-\pi/4 + k \pi)}\right)^2 = 9 e^{i (-\pi/2 + 2 k \pi)} = - 9 i$$ Since when does $i$ have a unique polar representation? Sep 23 comment What's the probability that I will earn \$25? @Sasha: Nice big fraction! Are you using arbitrary-precision rational numbers to compute$p$? Did you compute the Jordan canonical form of matrix$P$? Sep 23 comment What's the probability that I will earn \$25? @DavidFaux: You have a total of $126$ states in your Markov chain. Make the $0$ state and the $125$ state absorbing, i.e., draw an arrow from themselves onto themselves, so that once you get to either $0$ or $125$, you stay there forever. They are sinks. Since you can play forever, at some point you should observe that probability is concentrating around the two sinks. To see this, build a $126 \times 126$ tridiagonal matrix that models this phenomenon and compute its 100th or 1000th power. Sep 23 comment What's the probability that I will earn \$25? You can use Markov chains to model this problem. Take a look at: mathpages.com/home/kmath084/kmath084.htm Sep 22 comment Boy and Girl paradox @Gerenuk: One picks the uniform probability mass function (pmf) because it maximizes entropy. Thus, if we have no information at all, we assume a uniform pmf over$\Omega$. If you tell me that one of the children is a boy, then one of the points in the sample space is eliminated and the pmf is updated as we assume a uniform pmf over$\Omega'\$. This is a Bayesian interpretation of the problem. Would be interesting to think of a Frequentist interpretation. Sep 22 comment Boy and Girl paradox @Gerenuk: By "first child" and "second child" I meant "1st child that was born" and "2nd child that was born", i.e., I was referring to chronological order. The order in which you observe them does not change their dates of birth ;-) Sep 22 comment How to divide currency? @Auke: Ill-posed problems cannot be answered mathematically, but one can point out why they're ill-posed and try to steer the OP towards well-posed problems. I suggested a cost function at least. You just whine. If you dislike my answer so much, just downvote it.