A group of $n \ge 10$ people are numbered from $1$ to $n$ by their height, such that the height of the $i$ person is $i$. They are waiting in a straight line at the bank (one person in front of the other), with all orderings of the people equally likely. A person can see ahead to the front of the line if they are taller than everyone in front of them.
Let $Y_i$ be the number of people who are blocking the view of the $i$ person (that is, taller than him and standing in front of him in the line). for $1 \le i < n$, find $Cov(Y_i,Y_{i+1})$.
I found that the distribution of $Y_i$ is $Bin(n-i,\frac{1}{2})$, but I'm pretty stuck from there. Any ideas?