Rod Carvalho
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 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 answered Maximizing and minimizing Var(X) Sep 30 revised What kinds of initial value problems can have superposition of zero state response and zero input response? added 4 characters in body 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 revised Summation of a finite series involving permutations. edited body 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 answered I don't understand $\sqrt{-9i}$. Sep 23 answered Noise sensitivity of Boolean functions Sep 23 revised Find the 2nd order Taylor Polynomial of y(x) about x = 0, given: fixed some of the latex and typos Sep 23 suggested approved edit on Find the 2nd order Taylor Polynomial of y(x) about x = 0, given: Sep 23 suggested rejected edit on Show that the following is indeed a mass function for R.V. $Y$ which can take values $2^n$ and $-2^n$ with probability $\frac{1}{2^{n+2}}$ Sep 23 answered What's the probability that I will earn \$25? 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.