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Oct
2
comment Transform uniform distribution to normal distribution using Lindeberg–Lévy CLT
@cardinal: I tried Box-Muller, however i was not able to shift the median like with Marsaglia! And if i think about the scenario: in the time i compute 1.000 uniform numbers i will need... 10 normal ones and i am confident, that i will be have with this :)
Oct
2
comment Transform uniform distribution to normal distribution using Lindeberg–Lévy CLT
@Gortaur: I have a solution - please have a look at my question which is edited now.
Oct
2
comment Transform uniform distribution to normal distribution using Lindeberg–Lévy CLT
@cardinal: Found the solution - look at my original question ;)
Oct
2
comment Transform uniform distribution to normal distribution using Lindeberg–Lévy CLT
@cardinal: I need this only 10 times at the beginning of the game and maybe in really special circumstances and therefore efficiency is not that important. ;)
Oct
2
comment Transform uniform distribution to normal distribution using Lindeberg–Lévy CLT
I must confess, that adding a scalar $a$ was my first idea, however my algorithm seems buggy and it doesn't work like expected. Furthermore, debugging my code revealed that i am getting sometimes numbers $\leq 0$ which is weird. Any suggestions what i can do?
Sep
17
comment Inductive proof for the Binomial Theorem for rising factorials
Interesting way of prooving this, however i have to do this via induction. Still thanks for sharing the idea.
Aug
18
comment How to transform/expand a simple sum to prove equality of two sets?
Thanks for these hints. I will try now to check for equality on my own and i will try to understand the manufacturing of this explicit formula :-)
Aug
18
comment How to transform/expand a simple sum to prove equality of two sets?
Prooving this one should be not that difficult however it is not clear to me how to develop this term out of the sum of the powers of $-1$. That is the point - i would like to know how you have seen this!
Aug
18
comment How to transform/expand a simple sum to prove equality of two sets?
To be honest i do not see why you need to use $(-1)^{i+1}$ instead of $(-1)^i$ - the pattern seems clear to me, but the only reason to use $i+1$ seems to be to "heal" the problem to get to this pattern, isn't it that?
Aug
18
comment How to transform/expand a simple sum to prove equality of two sets?
@André Nicolas: It is true that $(1-(-1)^n)/2$ has this same property, but what is the way to get to this assumption?
Aug
15
comment Proof that $\mathbb{Z}$ has no zero divisors
Sorry for the confusion, but i have now understood this one. Can you explain me more detailed why do you use the term ring and not just the set of integers?
Aug
15
comment Proof that $\mathbb{Z}$ has no zero divisors
@Carl Mummert: I've added the rules i should base my proof on.
Aug
15
comment Proof that $\mathbb{Z}$ has no zero divisors
@Arturo Magidin: $\mathbb{Z}$ are normal integers $\{\cdots,-2,-1,0,1,2,\cdots\}$ with the "normal" multiplication like every knows it.
Aug
15
comment Proof that $\mathbb{Z}$ has no zero divisors
@Carl Mummert: I often look back :-) What other ideas do you have?
Jul
16
comment Computation of characteristic polynomial fails for me
@Theo Buehler: Thanks for the help - und danke sehr ;)
Jul
16
comment Computation of characteristic polynomial fails for me
@Theo Buehler: I am not given any specific matrix. The exercise is to prove the correctness of the relations... might it be true that $c_{n-1}$ can be computed this way and the other parts like $c_1$ not? Therefore i could proove the correctness of this without havong a look at $c_1$ if e.g. i let $n=3$.
Jul
16
comment Computation of characteristic polynomial fails for me
Understood. I don't know why i haven't seen this before! But is there any other algorithm or any other solution to make this one "really" recursive? This is just what was given to us in a lecture.
Jul
3
comment Proof that a linear transformation is isomorphic
@Andrea Mori: Ok, the rows of the matrix are the two vectors, therefore we have ((1, 1), (-1,1)) and the determinant thus equals 2. But we haven't worked with determinants yet and i do not know what i can do with this result.
Jul
3
comment Proof that a linear transformation is isomorphic
@zulon: That's one of conditions in the answer for Andrea Mori! Therefore there is something i have already understood.
Jul
3
comment Proof that a linear transformation is isomorphic
@Andrea Mori: I thought that the determinant can be computed for quadratic matrices, however the one here (x-y, x+y) is a 2x1 vector, or do i fail again?