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Jul
28
answered Problem on energy of a Discrete Galerkin Method
Jul
28
comment Is it possible to determine the average and median if we only have the upper part of a bell curve?
Okay maybe I get it. We should take the scores of the top 800, assume that 800 equals $x$% of the total number of players and derive the mean and variance for a normal distribution that is matched to the given data?
Jul
28
comment Is it possible to determine the average and median if we only have the upper part of a bell curve?
I'm not sure I fully get the question. You want to take the information about the top 800 to deduce a suitable normal distribution for all 9.3 million player? What should be done with the statistic from dota2toplist.com/statistics ? It seems like an interesting problem, but sadly I don't fully get your question.
Jul
28
reviewed Approve suggested edit on Evaluate $\int_0^\infty\frac{dl}{(r^2+l^2)^{\frac32}}$
Jul
28
comment Characteristic polynomial and eigenvalues of a $3 \times3$ matrix.
$(1-x)((-2-x)(1-x)+3(-(-2-x)3 =-(1-x)^2(2+x)+9(2+x)=(2+x)(9-(1-x)^2)$. Seems like this is easier to analyze w.r.t the roots. (I used $x$ instead of $\lambda$ because i was lazy.)
Jul
28
comment Characteristic polynomial and eigenvalues of a $3 \times3$ matrix.
According to Wolfram Alpha your calculation seems to be wrong
Jul
28
revised Characteristic polynomial and eigenvalues of a $3 \times3$ matrix.
changed latex notation
Jul
7
comment How to denote matrix when writing equation for exam
I agree with this. Make it as clear as possible, e.g. "Find $x \in \mathbb{R}^n$ such that for $A \in \mathbb{R}^{n\times n}$ and $b \in \mathbb{R}^n$ we have $Ax=b$" Here you even can skip the bold letters.
Jul
7
comment Can someone suggest a function to achieve this graph?
Also possible: $\sin(x)$ between $0$ and $\pi/2$. See Wolfram alpha for a plot. Correctly scaled, it should be $1+99\cdot sin(\pi x/224)$ from $0$ to $112$
Jul
7
comment Can someone suggest a function to achieve this graph?
As @Deepak has already pointed out, for discrete jumps you can use the floor function.
Jul
7
answered Can someone suggest a function to achieve this graph?
Jul
7
comment Can someone suggest a function to achieve this graph?
Nice question, I'll prepare several different approaches.
Jul
7
comment What is the variance of an arbitrary “good” function of several independent normally distributed random variables
Well this looks similar en.wikipedia.org/wiki/…
Jul
7
answered Alternating test
Jul
7
comment Alternating test
@DanielFischer So the question / goal is to show monotonicity? Thank you!
Jul
7
comment Alternating test
I don't fully understand the question. You know that $(n^3+n+1)/\sqrt{2n^7+n^5+1}$ converges to zero and you have an alternating series, thus you get convergence of the series. What to you mean with "can't figure out how to prove easily the decreasing of the sequence"? You already stated in the beginning of the sentence that the sequence converges to zero. Seems like I am not smart enough to understand you question / goal.
Jun
26
reviewed Approve suggested edit on Find the inflection points in the graph
Jun
26
reviewed Approve suggested edit on Some questions in set theory about belonging
Jun
19
awarded  Custodian
Jun
19
comment Probability of the same position!
Thank you, I fixed that.