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| bio | website | None |
|---|---|---|
| location | Atlanta, GA | |
| age | 26 | |
| visits | member for | 8 months |
| seen | Apr 18 at 0:59 | |
| stats | profile views | 30 |
I am a Ph.D. student in Operations Research at the Georgia Institute of Technology. I am an avid user of C++, Mathematica, and LaTeX. I benefit a great deal from answers on the Stack Exchange network, and I hope to contribute as much as I can to the growth of this great community.
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Feb 13 |
answered | Show that each of the following equations has a solution of the form $u(x,y) = f(ax+by) $ for a proper choice of constant $a,b$. |
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Feb 10 |
comment |
The Probability of an event occuring an exact amount of times Think about how you answered question 1, and you will see that $\binom{40}{2}$ is not giving the same information. If exactly 2 people share the same birthday, that means that the remaining 38 people must have different birthdays from each other and from the two who have the same birthday. Think of a simpler case where you have three people, can you answer the question then? |
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Feb 10 |
answered | The Probability of an event occuring an exact amount of times |
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Feb 10 |
comment |
The Probability of an event occuring an exact amount of times If there are 40 people in the room, then there are anywhere between 1 birth day in the room (everyone has the same birthday) and 40 birth days in the room (everyone has a different birthday). Having only two people sharing the same birthday is the same as saying there are exactly 39 brithdays in the room. |
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Feb 6 |
comment |
Is the event $\{\max\{X_1,X_2\}=X_2\}$ measurable with respect to $\sigma(\max\{X_1,X_2\})$? @Ilya, what I mean to say is the following. Consider my example where I use exponential random variables with $\lambda=\mu$. If $F$ is the distribution function of $Y=\max\{X_1,X_2\}$ and $G$ is the distribution function of $Z=1_{\{X_1\leq X_2\}}$, then the joint distribution function $H$ of $Y$ and $Z$ is given by the product of $F$ and $G$. |
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Jan 29 |
comment |
Is the event $\{\max\{X_1,X_2\}=X_2\}$ measurable with respect to $\sigma(\max\{X_1,X_2\})$? @Ilya, I think your explanation matched what my intuition was telling me, but I had no idea how to make it rigorous. In the example that I was working, $X_1$ and $X_2$ were exponential random variables with rate $\mu$ and $\lambda$, respectively. The problem was to check the independence of $\max(X_1,X_2)$ and the indicator $1_{(X_1\leq X_2)}$. The random variables are independent if and only if $\lambda=\mu$. Someone presented a proof based on the reasoning in my question, and I couldn't verify the validity of this person's proof. |
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Jan 29 |
accepted | Is the event $\{\max\{X_1,X_2\}=X_2\}$ measurable with respect to $\sigma(\max\{X_1,X_2\})$? |
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Jan 28 |
asked | Is the event $\{\max\{X_1,X_2\}=X_2\}$ measurable with respect to $\sigma(\max\{X_1,X_2\})$? |
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Oct 3 |
comment |
Convergence in measure does not imply $L^1$ convergence Thank you very much. I was sloppy, and too quick to answer. I mostly work in probability spaces, hence finite measure spaces, so I did not proof my work correctly. My new answer should be correct. Sorry for the confusion. |
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Oct 3 |
revised |
Convergence in measure does not imply $L^1$ convergence Example was wrong |
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Oct 3 |
answered | Convergence in measure does not imply $L^1$ convergence |
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Oct 3 |
awarded | Organizer |
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Oct 3 |
revised |
Create a unique numbers Removed tags that do not seem appropriate. |
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Oct 3 |
suggested | suggested edit on Create a unique numbers |
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Oct 3 |
comment |
Create a unique numbers I recommend looking at this article on Multi-Valued Functions. I think this is the mathematical concept that you are looking for. You could also consider vector valued functions, which may also represent what you are looking for. I'm not entirely sure that you will have a nice inverse function, but I think you could at least use these functions to describe a suitable algorithm. |
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Oct 3 |
comment |
Uniqueness of Lebesgue integrable functions of two variables defined by integration properties. I think your answer is particularly interesting, since I encountered this idea while working on some probability problems. |
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Oct 3 |
accepted | Uniqueness of Lebesgue integrable functions of two variables defined by integration properties. |
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Oct 3 |
comment |
Uniqueness of Lebesgue integrable functions of two variables defined by integration properties. Yes, thank you for reading my mind. I've corrected it now. |
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Oct 3 |
revised |
Uniqueness of Lebesgue integrable functions of two variables defined by integration properties. Typo in integrals |
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Oct 3 |
asked | Uniqueness of Lebesgue integrable functions of two variables defined by integration properties. |
