200,819 reputation
17143315
bio website
location
age
visits member for 4 years
seen 47 mins ago

As somebody used to say:

Does research. Smokes. Battles administration. Smokes. Wishes he could stop battling administration so that he could have more time to do research. Smokes some more.

The same. Except I do not smoke.


Dec
11
answered Uniform continuity of $f(x)=x^{\frac{2}{3}}\log x$ on $[0, \infty)$
Dec
11
comment Calculate. $\int_0^{\frac \pi 6}\cos 3x\ dx$
The trouble is that your answer leads the OP to believe that they should avoid considering directly a primitive of $x\mapsto\cos(3x)$. I believe this is a disservice to the OP since the opposite is true, they should be able to compute on the spot a primitive of this function, without preliminarily "simplifying the integral".
Dec
11
revised How to Obtain the conditional random variable with inequality in the conditional random variable
added 35 characters in body
Dec
11
revised How to Obtain the conditional random variable with inequality in the conditional random variable
added 35 characters in body
Dec
11
comment Calculate. $\int_0^{\frac \pi 6}\cos 3x\ dx$
Sorry but this seems at best anecdotal. Much better to enable the OP to compute a primitive of the function without remembering this trick.
Dec
11
comment How to Obtain the conditional random variable with inequality in the conditional random variable
Hmmmmm... See Edit.
Dec
11
revised How to Obtain the conditional random variable with inequality in the conditional random variable
added 69 characters in body
Dec
11
revised How to Obtain the conditional random variable with inequality in the conditional random variable
added 69 characters in body
Dec
11
comment How to Obtain the conditional random variable with inequality in the conditional random variable
No. The conditioning event is $[Y\gt X]$, not $[Y\gt X=x]$. Did you manage to compute $P[X\gt x,Y\gt X]$ and $P[Y\gt X]$?
Dec
11
comment Mean and Variance of a functions of uniform random variable - as applied to a limiter
You are welcome. +1. And I like that you leave something to do to the OP, so that they can check they understand the solution.
Dec
11
comment how does $\sum_{n=0}^{\infty} (-1)^n \frac{1}{1+n}$ diverge?
Which sources? The series does converge (not absolutely, though).
Dec
11
comment E(X|X+Y) X,Y iid exp(-1)??
Since A and B are events and X and Y are random variables, the phrase "Let A=X and B=X+Y" is dubious.
Dec
11
answered E(X|X+Y) X,Y iid exp(-1)??
Dec
11
comment There exists no continuous function $f:\mathbb{R}\rightarrow\mathbb{R}$ with $f=\chi_{[0,1]}$ almost everywhere
OK. This should come soon.
Dec
11
comment How to Obtain the conditional random variable with inequality in the conditional random variable
Sorry? What am I supposed to ignore?
Dec
11
comment Mean and Variance of a functions of uniform random variable - as applied to a limiter
Right. Another thing: rereading the question, it is obvious that Y is symmetric hence E(Y)=0 and the real job is to compute E(Y^2).
Dec
11
comment counterexample for Dominated Convergence Theorem
If the functions $f_n$ are not in $L^1$ the integrals $\int f_n$ are not even defined hence the theorem becomes pointless.
Dec
11
comment There exists no continuous function $f:\mathbb{R}\rightarrow\mathbb{R}$ with $f=\chi_{[0,1]}$ almost everywhere
"there were no ways to could ask something on the other page" Why is that? Can't you comment?
Dec
11
comment Prove that every finite group G contains a (unique) soluble normal subgroup N such that G/N has no nontrivial abelian normal subgroups.
@NickyHekster This was explained in the comments.
Dec
11
comment Mean and Variance of a functions of uniform random variable - as applied to a limiter
One might recommend to use the PDF of U, otherwise one needs to compute the PDF of X, a cumbersome and not useful task.