Hi all
I am looking for a simple way to show that the mean of the Cauchy distribution us undefined. This is because this integral diverges:
\underset{-\infty}{\overset{\infty}{\int}}\frac{x}{x^{2}+a^{2}}dx
Now, I know one proof which replaces the limits of integration with -x1 and x2. After...
This wasn't obvious to me.
From my book. We have,
p(x)=\begin{cases}
\frac{1}{2} & -2\leq x\leq-1\,\textrm{or}\;1\leq x\leq2,\\
0 & \text{otherwise~}.\end{cases}
So, the kth moment is given by
M_{k}=\frac{1}{2}\int_{-2}^{-1}x^{k}dx+\frac{1}{2}\int_{1}^{2}x^{k}dx
So, obviously...
Thanks. I considered arctan already, but since this function goes momentarily vertical zero arctan doesn't work. Same with a Gompertz function and Richards curve (I think). Also, this function appears to be odd, so that would rule out a Gompterz function also. Are there Sigmoid curves that are...
Hi all
What are some candidate functions f(x) that satisfy these conditions:
1. domain of f is R
2. image of f is (-1,1)
2. Smooth and continuous everywhere
3. first derivative undefined at x=0
4. f(x)-->1 as x--> inf
5. f(x)-->-1 as x--> -inf
Thanks
LR