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Nov
13
answered About a maximal inequality
Nov
13
comment Determining a function from a graph
You could do polynomial interpolation with degree $10-1=9$. Excel has this built in.
Nov
13
comment $\delta$ and $\epsilon$ in the continuity definition
Arbitrarily small means that you can pick an arbitrarily small value, not that $\epsilon$ as a number is arbitrarily small in the same sense that a number is "infinite." Look at how I showed the example function is discontinuous.
Nov
13
answered $\delta$ and $\epsilon$ in the continuity definition
Nov
12
asked Directed Graph (Lattice) Integration
Nov
12
comment How to show $\sum_{i=1}^{n-1} \frac{i(n-2)!}{(n-1-i)!n^{i+1}} \sim 1/n$
Your guess seems reasonable numerically. If you plot the fraction inside the sum for fixed $n$ in terms of $i$, it peaks very quickly in $i$ and then goes down rapidly. Try using Stirling's formula to investigate what's going on for small $i$, particularly it looks like $i\approx \sqrt{n}$ is the sweet spot.
Nov
12
comment Stochastic intensity poisson process
Maybe I'm not understanding your question. If you're asking whether their probability measures on $\Omega$ are the same then, no they won't be in general. But on $\mathbb{R}$ they would be (assuming the prior comment). In other words their laws are weakly equal to each other on $\mathbb{R}$, but not strongly on $\Omega$.
Nov
12
comment Stochastic intensity poisson process
If jumps are independent, and have the same waiting time, then why would they be different processes? I mean, why does it matter what the underlying sigma algebra is as long as $\mathbb{P}(X_t\leq s)$ is the same for both, along with marginals?
Nov
12
comment Let $(X_1,…,X_r) \sim Mult(n,r,p_1,…,p_r)$. Determine whether X1 and X2 are independent.
Just read this section here on the mass function: en.wikipedia.org/wiki/Multinomial_distribution#Specification
Nov
12
comment Let $(X_1,…,X_r) \sim Mult(n,r,p_1,…,p_r)$. Determine whether X1 and X2 are independent.
@user181928: you need to analyze the multinomial distribution more closely. What must $X_1+X_2+\cdots+X_n$ satisfy?
Nov
12
revised Let $(X_1,…,X_r) \sim Mult(n,r,p_1,…,p_r)$. Determine whether X1 and X2 are independent.
added 6 characters in body
Nov
12
answered Let $(X_1,…,X_r) \sim Mult(n,r,p_1,…,p_r)$. Determine whether X1 and X2 are independent.
Nov
12
comment On Collatz conjecture
@GogiPantsulaia: Perhaps, if you formalize what it means for $x$ to be random in the integers. There's no uniform distribution, so presumably you'd need to prove the result for all finite intervals $[1,N]$.
Nov
12
revised On Collatz conjecture
deleted 222 characters in body
Nov
11
answered Why is empty product defined to be $1$?
Nov
11
answered On Collatz conjecture
Nov
11
answered Open mathematical questions for which we really, really have no idea what the answer is
Nov
10
comment Show that if mean of $X_i = m,$ Then $P(\frac{X_1 + \ldots + X_n}{n} < m/2) \to 1$ as $n$ is large.
This is completely false as it contradicts the strong law of large numbers. Where did you get such a statement/problem?
Nov
6
comment Limit of integral over set measurable
@user126033: then you can prove this version of it from scratch as outlined above. The result is trivial for intervals by fundamental theorem of calculus.
Nov
6
answered Limit of integral over set measurable