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Jun
11
comment Example of periodic $f\left(x\right)+xg\left(x\right)$, where f is even function and g is periodic
$f(x)=cos(x)$ and $g(x)=sin(x)/x$.
May
30
comment Which of two quantities is greater?
Thanks @Michael. For the comparison of these functions, (say $f$ and $g$), I can simply show $f(0)=g(0)$, the slope of $g$ is more negative than that of $f$ and that $g$ is decreasing throughout $(0,1)$. Is that right or is there a more compact way of doing this?
May
30
comment Which of two quantities is greater?
Hi. I have a follow-up question: I need to show $(x-y)^{((x-y)/(2x-y))}\times (x+y)^{((x)/(2x-y))}>x$. I am not sure how the AM-GM inequality leads to this, as the GM is on the LHS?
May
21
comment Computing expectation of a function of two random variables
@zoli: Yes, there are $N-1$ independent draws and the $N^{th} $ is dependent on the previous draws. Your understanding is right.
May
21
comment Computing expectation of a function of two random variables
@zoli: Why not? I never said within array $X$, the draws are independent. $x_n(\omega)=S_x-\sum_{i=1}^{N-1}x_i$ for all $\omega$.
May
21
comment Computing expectation of a function of two random variables
@zoli: One number in the array. Distribution with finite support on the real line.
Apr
24
comment Continuity of optimisation problem
@calculus: I have solved $F(z)$, the issue is about the continuity of $F(z)$. The solution exhibits a discontinuity at $z=0$. My question is for what classes of optimisation problems will such a discontinuity not be there?
Apr
7
comment Bounding $x^\top Ay/x^\top y$
@Tryss: By assumption, they are not orthogonal. Clarified.
Apr
2
comment Is the optimum of this problem unique?
Thanks Hans. I guess a sufficient condition for interior solution will be: $\sum_j b_j \log(a_j/b_j)-(\sum_j b_j)\log(a_i/b_i)<x$, for all $i$.
Apr
2
comment Is the optimum of this problem unique?
I know that, but how is the minimum dependent on $a_i$s and $b_i$s?
Mar
11
comment Poisson processes and coin flips
I guess by 'flipped', he means tossed and not simply turned upside down. Not sure though, but the first sentence says "is flipped and lands on...". In that case, the answer would remain $p$.
Feb
16
comment Proving a function of matrix is convex
Thanks Michael. I get the determinant of the Hessian to be $-\frac{y^2}{(a-1)^4}$, which is negative?
Feb
16
comment Proving a function of matrix is convex
I meant $f$ is a function of both $A$ and $b$. However I am struggling even with the case when $f$ is only a function of $A$.
Dec
20
comment Joint distribution of arrival times in Poisson process
Thanks Did. I guess it would be $f_{S_A}(t_1)\times f_{S_B}(t_2-t_1)$, with the $S_A$ being Erlang. Correct?
Sep
16
comment How to solve integrals of the form $\int u^{-\alpha} e^{-\beta u} du$?
Let us continue this discussion in chat.
Sep
15
comment Is there a closed form solution for this differential equation?
@MhenniBenghorbal: Thanks for the comment. Could you give me some guideline as to how to go about approximating ODEs?
Sep
15
comment Is there a closed form solution for this differential equation?
The main confusion being exp integral is defined as a definite intgeral and we have indefinite integrals in our equations.
Sep
15
comment Is there a closed form solution for this differential equation?
Thanks @Chinny. There is a typo which gets repeated - $k_2t$ in place of $k_3 t$ in the exponent. Also I do not understand how you used the def. of exp. integral. Could you pl. correct and elaborate? Thanks :)
Sep
15
comment How to solve integrals of the form $\int u^{-\alpha} e^{-\beta u} du$?
Hi @ClaudeLeibovici: My main ques. is how we can move from an indefinite integral to a definite integral, as is the case in the definition for $E_\alpha$.
Sep
15
comment How to solve integrals of the form $\int u^{-\alpha} e^{-\beta u} du$?
@ClaudeLeibovici: No, from the Wiki defn, I do not see how you arrive at the transformation from gamma to exp.