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seen Feb 10 at 2:34

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 suggested edit on Find the 2nd order Taylor Polynomial of y(x) about x = 0, given:
Sep
23
suggested suggested 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.
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.