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visits member for 3 years, 6 months
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I have a Ph.D. with a minor in mathematics and a major in statistics.


2d
revised Prove $\mathbb{R}^k$ is complete w.r.t. the maximum norm
corrected LaTeX and changed the title, since the specific norm has a name
2d
revised $\epsilon$-$\delta$ limit proof that $\lim_{n\to \infty}\frac{n^2-n+2}{3n^2+2n-4}=\frac{1}{3}$
edited title
2d
revised Determine the expected value of a geometric distribution given some generic underlying distribution.
edited body
2d
comment Determine the expected value of a geometric distribution given some generic underlying distribution.
It's finally occured to me the next day that there is a simple way to show that $\Pr(N>n) = \dfrac 1 {n-1} - \dfrac 1 n$ without enumerating any permutations. I have now added that as another postscript in my posted answer. See below. ${}\qquad{}$
2d
comment Determine the expected value of a geometric distribution given some generic underlying distribution.
@chibro2 : Indeed, the expectation is infinite.
2d
revised Determine the expected value of a geometric distribution given some generic underlying distribution.
added 319 characters in body
2d
revised $s \in L^{1}(H)$ $\iff$ $s=\sum_{i=0}^\infty x_{i} \otimes y_{i} $
||x|| changed to \|x\|
Dec
17
revised $E(g(X)), E(g'(X)) <\infty $ implies $\lim_{x\rightarrow \infty} f(x)g(x)= 0$ ($f$ is the density of $X$)?
added 22 characters in body; edited title
Dec
17
comment Determine the expected value of a geometric distribution given some generic underlying distribution.
OK, now I have fully solved the problem. It turns out that the distribution of $N$ does not depend on which function $F$ is, as long as $F$ is a continuous c.d.f. We get $\Pr(N=n)=1/(n(n+1))$. ${}\qquad{}$
Dec
17
comment Determine the expected value of a geometric distribution given some generic underlying distribution.
OK, now I have fully solved the problem. It turns out that the distribution of $N$ does not depend on which function $F$ is, as long as $F$ is a continuous c.d.f. We get $\Pr(N=n)=1/(n(n+1))$. ${}\qquad{}$
Dec
17
revised Determine the expected value of a geometric distribution given some generic underlying distribution.
added 155 characters in body
Dec
17
comment Determine the expected value of a geometric distribution given some generic underlying distribution.
@chibro2 : Say you have two random variables $A$ and $B$, and they both have the same continuous distribution (and "continuous" imples $\Pr(A=B)=0$) and they're independent. Then $\Pr(A>B)=\Pr(B>A)$ because the distribution of the pair $(A,B)$ is the same as the distribution of the pair $(B,A)$. That is symmetry. ${}\qquad{}$
Dec
17
revised Determine the expected value of a geometric distribution given some generic underlying distribution.
added 155 characters in body
Dec
17
comment How do I prove that there doesn't exist a set whose power set is countable?
en.wikipedia.org/wiki/Cantor%27s_theorem ${}\qquad{}$
Dec
17
comment Determine the expected value of a geometric distribution given some generic underlying distribution.
How you compute them would depend on what the c.d.f. $F$ is. You can say $\displaystyle\operatorname{E}(X_1)=\int_{-\infty}^\infty x\,dF(x)$ regardless of whether there is a p.d.f., but how you compute that depends on which function $F$ is. ${}\qquad{}$
Dec
17
revised Determine the expected value of a geometric distribution given some generic underlying distribution.
added 3 characters in body
Dec
17
comment Double integral with two parameters $\int_{x_1=1}^{x_2=2}\int_{y_1=0}^{y_2=x}\arctan\left(\frac{y}{x}\right)\,dx\,dy$
Your MathJax technique could use some work. Please look at my edits. In particular "a\arctan b" yields $a\arctan b$ with proper spacing between $\arctan$ and $a$ and $b$ (and also it's not italicized). Similarly with \ln. And \text{} is useful. ${}\qquad{}$
Dec
17
revised Double integral with two parameters $\int_{x_1=1}^{x_2=2}\int_{y_1=0}^{y_2=x}\arctan\left(\frac{y}{x}\right)\,dx\,dy$
added 22 characters in body
Dec
17
answered Determine the expected value of a geometric distribution given some generic underlying distribution.
Dec
17
comment Determine the expected value of a geometric distribution given some generic underlying distribution.
I find this erroneous. I'll post an answer.