Recent content by forumfann

The x-axis and y-axis are interchanged in the figure by running the following MATLAB function I wrote. Could anyone help me to get it corrected? Thanks in advance for any helpful answer. function axislabeling(n) x=1:1:n; y=1:1:n; z=zeros(n,n); for i=1:n for j=1:n z(i,j)=i; end end...

Let f(x):=\frac{1+(1+x)^{4}+(1-2x)^{4}}{\sqrt[4]{1+x^{4}}} and x_{0} be the minimizer of f(x). Is it true that x_{0} is the maximizer of g(x):=\frac{1+(1+x)(1+x_{0})^{3}+(1-2x)(1-2x_{0})^{3}}{\sqrt[4]{1+x^{4}}}? Thanks in advance for any helpful answer.

In many statements in probability, there is an assumption like bounded fourth moment, so is there any random variable which has unbounded fourth moment?

In fact, I have checked the cases of n=1 through 1000, and it holds for all the cases. But I still don't know how to show it in general. Any other help?

The LHS is always positive for x\in(0,1). That is fine.

When k=0, x^k(1-x)^{2n-k} goes to 1 as x goes to 0, so 1-\sum_{k=0}^{n}\left(\begin{array}{c} 2n\\ k\end{array}\right)x^{k}\left(1-x\right)^{2n-k} tends to 0 as x goes to 0 because the other terms with k>0 has a factor x. But thanks anyway.

Could anyone help me on this question? Is it true that \sum_{k=n+1}^{2n}\left(\begin{array}{c} 2n\\k\end{array}\right)x^{k}\left(1-x\right)^{2n-k}\leq2x for any x\in(0,1) and any positive integer n? Any help on that will be greatly appreciated!

Thanks. But then is it true that P\left(x_{1}+x_{2}+x_{3}+x_{4}+x_{5}+x_{6}<3\delta\right)\leq2P\left(x_{1}<\delta\right) for any \delta>0 ?

Suppose x_1,x_2,x_3,x_4 are non-negative Independent and identically-distributed random variables, is it true that P\left(x_{1}+x_{2}+x_{3}+x_{4}<2\delta\right)\leq2P\left(x_{1}<\delta\right) for any \delta>0? Any answer or suggestion will be highly appreciated!

Yes, the variables are independent. But what are the standard procedures? It there a easier way to get the pdf if one has more random variables than three?

Could anyone help me figure out the the probability density function (pdf) of |X|^(1/2)+|Y|^(1/2)+|Z|^(1/2) if X, Y and Z are distributed normally with mean 0 and variance 1, N(0,1) ? Thanks in advance.

If t-t_{1} and t-t_{2} are equal to 2pi, pi or 0 ? Then the left hand side of the given inequality is r_1+r_2, which is less than the right hand side of the given inequality that is not larger than r_3+r_4. Thus the claim is automatically true. I think what makes it possible to be true...

Could anyone help me on this, Is it true that for any given r_{1},r_{2},r_{3},r_{4}>0 and t_{1},t_{2},t_{3},t_{4}\in[0,2\pi) if r_{1}\left|\cos(t-t_{1})\right|+r_{2}\left|\cos(t-t_{2})\right|<r_{3}\left|\cos(t-t_{3})\right|+r_{4}\left|\cos(t-t_{4})\right| for all t\in[0,2\pi) then...

I am confused on a basic probability inequality, could anyone help me on this: If X>Y>t, then is P(X>t) larger or smaller than P(Y>t)? Thanks

This a problem that I was curious about, because we know that ||x||_{m}\leq||x||_{1} for any positive integer m, and then I wondered if it is true for any p\geq1. But it would be great if one can show the following: ||x||_{p}\leq||x||_{1} for p\geq1, so could anyone help me on this?