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visits member for 2 years, 11 months
seen Aug 13 at 8:30

Jul
2
awarded  Popular Question
Jul
2
awarded  Curious
Jul
2
awarded  Inquisitive
Mar
31
asked Is this function monotonically non-decreasing?
Mar
28
revised Integral involving a confluent hypergeometric function
Improved readability of the answer by putting the mathematical symbols into LaTeX.
Mar
28
accepted Integral involving a confluent hypergeometric function
Mar
28
comment Integral involving a confluent hypergeometric function
I was just thinking about this question the other day, and, as you said, the trick here is the summation representation of ${}_1F_1$ (which I didn't think about when I posted the question -- it came up as a step in a long series of calculations in Mathematica). Anyway, thanks for your answer (I edited tiny bit of formatting for mathematical symbols).
Mar
28
suggested suggested edit on Integral involving a confluent hypergeometric function
Mar
27
accepted How to numerically evaluate the CDF of this random variable?
Mar
27
comment How to numerically evaluate the CDF of this random variable?
Ahh, I see -- there is $x-t$ in the binomial. I must say, this is a fiendishly clever answer. I never though of using generating functions for this (and, as the matter of fact, until now I didn't know what generating functions were good for other than exercises in a graduate probability class...) Thanks!
Mar
27
comment How to numerically evaluate the CDF of this random variable?
Thanks for the edit! I still have questions. First, what is $A_x$? It is summation over $x$ from $x=0$ to $x=m$? I summed it that way (using Mathematica) and it spat out an expression involving ${}_2F_1$...
Mar
26
comment How to numerically evaluate the CDF of this random variable?
Thanks for the answer. I understand the normal approximation for the binomial distribution, but am stuck on your first sentence. Writing out the sum $Y+Z$ as a convolution, I obtain the following: $$\sum_{t=0}^x\binom{n}{t}(p+q-pq)^t(1-p-q+pq)^{n-t}\binom{m-n}{x-t}q^{x-t}(1-q)‌​^{m-n-x+t}.$$ Since $1-p-q+pq=(1-p)(1-q)$, I can simplify the convolution as follows: $$\sum_{t=0}^x\binom{n}{t}(p+q-pq)^t(1-p)^{n-t}\binom{m-n}{x-t}q^{x-t}(1-q)^{m-x‌​}$$ but I can't get the expression in (1). Could please elaborate how you get there?
Mar
26
revised How to numerically evaluate the CDF of this random variable?
fixed typo
Mar
26
asked How to numerically evaluate the CDF of this random variable?
Feb
20
awarded  Popular Question
Jan
2
comment Does strong law of large numbers hold for an average of this triangular array containing “almost i.i.d.” sequences?
Thanks for your help, Alex and @Ahriman. I added the explanation of the origin of my random variable in my question. I don't think that it's possible to prove what I want...
Jan
2
comment Does strong law of large numbers hold for an average of this triangular array containing “almost i.i.d.” sequences?
Thanks for the counterexample. I added an explanation to my question as to where my random variables came from...
Jan
2
comment Does strong law of large numbers hold for an average of this triangular array containing “almost i.i.d.” sequences?
@Did Because it seemed correct at the time. Now that I know more, I reversed my acceptance (sorry, Alex Becker). This convergence and the triangular array business is pretty tricky, hence all my questions on it. However, I am learning... thanks for your help everyone! Btw, I edited the question, explaining where my random variables came from...
Jan
2
revised Does strong law of large numbers hold for an average of this triangular array containing “almost i.i.d.” sequences?
major changes based on responses and comments
Jan
1
comment Triangular arrays and almost sure convergence of row averages
Thanks for the answer, it's a nice counterexample. I am trying to think of cases when almost sure convergence might hold. For instance, your counterexample would not work if we made all the elements of the triangular array i.i.d. (not just within each row). Would the row average converge almost surely to $\mu$ in that case?