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 $p$).
PMF expectation and variance internet problem
Hint: $X-Y=X-(n-X)=2X-n$. We are familiar with the binomial random variable $X$, its distribution, its mean, its variance.