Let random variable $X$ be defined as the number of independent Bernoulli(p) trials required until we observe either two successes or two failures in a row. Find $P(X=n)$ for $n=2,3,4, \ldots$ Then find the expectation and variance of $X$.
Okay so since there has to be two successes or failures in a row, the trials have to alternate $SFSFSF...$ or $FSFSFS...$ until it comes upon two successes or two failures. I initially tried using the Negative Binomial Distribution here but I remembered that it doesn't take order into account so that wouldn't work. Then I tried breaking it up into if $n$ is odd vs. if $n$ is even but but I didn't really know where to go from there...