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Mar
31
comment If $x = \operatorname{argmin}_{x \in X} \lvert Ax - y\rvert^2$ does it mean that $Ax = \operatorname{Proj}_X(Ay)$?
is $X$ a vector space?
Mar
30
comment A multi-variant integration problem
This question will be closed unless you specify what you've tried. Saying it's "urgent" is irrelevant.
Mar
28
comment Mean-pressure of an acoustic wave
What is preventing you from evaluating the integral term by term? You know that $\phi=\omega t-K$, where $K$ is a constant (in time), so just evaluate each piece. $p_1$ is constant.
Mar
28
comment Conditional Brownian Motion
why did the conditioning on $W_u$ suddenly disappear in the second equality? Also why are you multiplying by $t/u$?
Mar
27
comment Calculate percentage given 25% percentile, 50% percentile, and 75% percentile
Do you know the total number of people who were solicited? Then perhaps you can assume that each person has probability $p$ of signing up, and you can solve for $p$ using your numbers.
Mar
27
answered Prove $\int_{a}^{b}{f(x)dx}>0$.
Mar
27
comment How can a set be a subset of a $\sigma$-algebra
it's perfectly fine if $S$ is a collection of subsets of $\mathcal{A}$.
Mar
24
comment Why Laplace transform equals zero if and only if $f(x)=0$?
Prove the statement for step functions, then simple functions and finally take a uniform limit of simple functions to show the result for all functions $f(x)$.
Mar
20
comment Central Limit theorem solving for n with absolute value
Do you understand the meaning of a $Z$ table? If you do, please write down the precise meaning of the numbers you see in your $Z$ table.
Mar
18
comment Method of solving no-homogeneous recurrence equation
Do you have other boundary conditions?
Mar
17
comment Understanding what paths,trails and circuits and cycles and walk length mean
Sorry I'm confused. In the definition of trail, they plainly state no edge is repeated. Whereas for a path, no vertex is repeated. They implicitly define a closed path as a path with no repeated vertex except for $x=y$ for start/end vertices.
Mar
17
comment A functional equation: $4f(x)^3 +f(3x)=3f(x)$
For my personal curiosity then, how would this work for: math.stackexchange.com/questions/957705/… which has only one solution, continuous or otherwise. I guess I'm just confused how it's easy as you claim without the usual clever manipulations and test values that go into solving these kinds of things.
Mar
17
comment Understanding what paths,trails and circuits and cycles and walk length mean
"Repeated" for the definition of a walk? They are referring to edges. So you can definitely visit vertices multiple times if they have more than one edge coming out of them. Think of "visiting no vertex twice" as a stronger condition than "visiting no edge twice." The former implies the latter but not the other way around.
Mar
17
comment Is there a smart way to compute $\sum^{25}_{k=0}\binom {3000}{k} p^k (1-p)^{3000-k}$?
@ajotatxe: sums of this type are Poisson, not normal.
Mar
17
answered Is there a smart way to compute $\sum^{25}_{k=0}\binom {3000}{k} p^k (1-p)^{3000-k}$?
Mar
17
comment Understanding what paths,trails and circuits and cycles and walk length mean
So for part (b), on the subject of a cycle, they meant that no vertex occurs twice, except for $x=y$. Then it looks like everything is consistent.
Mar
17
comment Definition of limiting distribution in a Markov chain — why do we condition on the initial state?
If the chain is finite and irreducible, then the initial state does not matter for the definition (the limit is the same for all initial states). On the other hand, if the chain is reducible, you could have multiple limit distributions, which would arise differently depending on which component you start in.
Mar
17
comment Understanding what paths,trails and circuits and cycles and walk length mean
Somewhere before this definition should be a definition for a "walk." It looks like there's an issue with whether or not the vertex $x$, which is the starting vertex of the walk, is or isn't included in the vertex list.
Mar
17
comment A functional equation: $4f(x)^3 +f(3x)=3f(x)$
Isn't this just saying "find all solutions to the resulting equations?" I mean, you could say the same thing for any functional equation but it gives nothing toward actually solving it.
Mar
17
comment Uniform convergence in series definitions of functions
Anything with a singularity.