A set of binary data can have either a 1 with probability or a 0 with probability . A set of outcomes that have to same values is referred to as a run (i.e the set 1,1,0,1,1,1,1 where the first run with have 2 values, the second run would have 1, the third of length 4, and so on).
A) Find the expected length of the 1st run
B) Find the expected length of the 2nd run
B) I would think it would be an identical to part A), but I'm unsure of that.