Probability exercise Bernoulli. Probability random signals. Im late I have no idea to start and this is for tomorrow. I was on training and have no break to do this work. I do this.You are an Internet savvy and enjoy watching video clips of your favorite artists. You normally download video clips from the Web site http://www.coolvideos.com. The probability that you can connect to this site in any one attempt is $p$. Define $$X as the number of successes and $Y$ as the number of failures in $n$ attempts.
(a) Find the probability mass function (PMF) of $Z=X−Y$.
(b) Find $E[Z]$ (in terms of $n$ and $p$).
(c) Find Var[Z] (in terms of n and p).
A) This is what I attempted
Pr [z=k]= Pr [2x-n=k]= Pr [x=((n+k)÷2)]=?

You have started essentially correctly. We have $X-Y=X-(n-X)=2X-n$. So 
$$\Pr(Z=k)=\Pr(2X-n=k)=\Pr\left(X=\frac{n+k}{2}\right)=\binom{n}{(n+k)/2}p^{(n+k)/2}(1-p)^{(n-k)/2}.$$
This makes sense only when $-n\le k\le n$ and $n$ and $k$ are of the same parity (both even or both odd). 
The rest of the problems are more mechanical. 
$$E(Z)=E(2X-n)=2E(X)-n=2np-n.$$
$$\text{Var}(X)=2^2\text{Var}(X)=4np(1-p).$$
