Here is a question I am trying to solve:
An unfair coin with probability $p$ for head is thrown $16$ times in a row. Find the expectation of the number of streaks of heads.
My thoughts: The result of the sequence number of streaks of heads with length $n$ is $(n-1)(1-p)p + p$.
Starting from the second throw, the probability that it starts a new H streak is $P(\text{previously T})P(\text{now H}) = (1-p)p$, using linearity of expectation it is $(n-1)(1-p)p$; plus the first coin is $p$ contributed by H.
Nonetheless I'm not sure how to finish. Any help would be appreciated.