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Apr
22
comment compute probability density function of a bivariate function without sampling
@kensaii indeed this is a convolution. If you cannot solve for one in terms of the other, this is not really usable.
Apr
21
comment compute probability density function of a bivariate function without sampling
why not condition on $X_2$?
Apr
21
comment compute probability density function of a bivariate function without sampling
what do you know of the relationship between $X_1,X_2$? E.g. if they are independent, $g(x_1, x_2) = f_{X_1}(x_1) \times f_{X_2}(x_2)$...
Apr
20
comment Let $(X, Y )$ be a random pair with the density $f(x,y) = c(y-x)^2, 0<x<y<1$ and $0, elsewhere$ for some constant $c > 0$.
@Slae no :) the upper limit should be constant, otherwise your integral ends up as a function of $y$. Why don't you draw the region to figure out which value to pick?
Apr
15
comment Optimization question related to calculus.
@almagest sorry fixed
Apr
15
comment Definition of matrix transformation
i think so :) that's indeed a common definition
Apr
14
comment Linear Algebra: showing that $\langle x,y\rangle$ is an inner product on Rn.
yes, you got it right
Apr
14
comment You can always delete a vertex from a tree $G$ such that the remaining connected components have size at most $|V(G)|/2$.
one hunch is try to a proof by induction, possibly deleting a leaf, but not sure if it will help.
Apr
14
comment What is the domain and range of the sum of two random variables?
@Did perhaps i see the difference -- you want to define $S(\omega) = X_1(\omega) + X_2(\omega)$ where all variables map from $\Omega^n$, but each $X_i$ only uses the $i$th coordinate. Why would this make impossible every simple operation? We just defined addition, you can define integration and scalar multiple and everything else analogously -- why does this cause a problem? Please understand, I am not arguing, just asking for clarification for my own education. Thanks
Apr
14
comment What is the domain and range of the sum of two random variables?
@Did i honestly don't understand how you can do it any other way -- the construction in the accepted answer uses product spaces as well, which is what i did here, and so do Artem Mavrin's remarks, and your comment seems to indicate that you agree. I fail to see the difference between that construction and the one in my answer.
Apr
13
comment How to evaluate the integral $\int_0^5 3x^2 dx $?
@AkivaWeinberger i did fix it, but in this setting, everyone will end up with the same one so the was not exactly misplaced
Apr
13
comment solve $\sin 2x + \sin x = 0 $ using addition formula
@N.F.Taussig fixed
Apr
12
comment orthonormal columns and linear independent vectors
Gram-Schmidt orthogonalization?
Apr
12
comment What is the domain and range of the sum of two random variables?
@user1770201 no contradiction, his last paragraph states in 5 lines what i wrote in 1
Apr
12
comment Finding the bound of a linear functional defined on $C[-1,1]$
oknp :) you can click edit and see how i did it so yours will look pretty next time. \left and \right constructs are floating in size and quite useful for such cases
Apr
12
comment How many non-negative integer solutions of $x_1 + x_2 + x_3 + x_4 = 28$ are there with $x_{1} \leq 6, x_{2} \leq 10, x_{3} \leq 15, x_{4} \leq21$?
@NoName not wrong, you can do it that way -- but this is a very common alternative.
Apr
12
comment What is the domain and range of the sum of two random variables?
@user1770201 this is a general definition
Apr
7
comment Show that $x^2 + y^2 + z^2 = x^3 + y^3 + z^3$ has infinitely many integer solutions.
another one just as obvious is $(0,0,0)$
Apr
7
comment Formula for the number of partitions of 2N elements
@ThomasAndrews yes, fixed thank you
Apr
7
comment Formula for the number of partitions of 2N elements
@ThomasAndrews fixed thanks