Consider a sequence consisting of symbols 1 (occurs with probability P) and 0 (occurs with probability Q, where Q=1-P). A run is a consecutive…

Consider a sequence consisting of symbols 1 (occurs with probability P) and 0 (occurs with probability Q, where Q=1-P). A run is a consecutive sequence of the same symbol. The length of the first run refers to how many times the first symbol appears consecutively at the start of the sequence before switching. Similarly, the length of the second run refers to the number of times the next different symbol appears before switching again. Find the expected length of the first and second run.