I think you should set the full path, before passing the argument it has to start with a ” before a space.
Switch to full stop after absolute path declaration – also set the working directory as you have to know where the program is.
You could also use the Perl Sub-Handlers list in the send_headers() sub-routine to look for special HTTP-Requests.
[The List sub-handler lets you catch certain requests]
And at some point of the code you could set it to HTML-Response.
And at last you might want to look at the WWW::Mechanize::LWP::UserAgent module – that class can change the HTTP user agent the LWP::Protocol object is using.

Q:

Expected value of a result of two independt random variables

I have a vector of negative, real values $x$ and a vector of non-negative values $y$. As you can see, I would like to compute their product.
For the’real’ part I can solve the problem quite easy
$E(x) = E[-x] = -E[x]$
or $E(x) = E(x^2) – E(x)$, as there are pairwise independent entries in the vector.
For the non-negative part I started to think about the convolution of two CDF’s.
$$F_{x*y}(t)=\int_{ -\infty}^{\infty}f_x(x)f_y(y)dx$$
That doesn’t look so bad. However, now I am stuck at the derivation, which involves
$$F_{x+y}(t)=\int_{ -\infty}^{\infty}f_x(x)f_y(y)dx$$
What is

the origin of that assumption

Thank you very much

A:

Your problem doesn’t require $x$ and $y$ to be independent.
For simplicity, let’s take $x$ to be $\mathcal N(0,1)$ and $y$ to be $\mathcal U(-1,1)$.
For $n\in\mathbb N$, the joint density of $(x,y)$ is:
\begin{align*}
f_{x,y}(