I need help with a question in my statistics book:
Given a positive integer $n$. We want to form an $n$-bit string. Each bit is independently assigned as a $0$ or $1$ (each with probability $0.5$). Find the expected value of the longest sub-string of $1$'s.
I know how to calculate expected values however in this context I'm so confused that I have no idea how to even begin. How do we go about this?
Any help is very much appreciated. Thank you.