I'm having a hard time solving this. I hope someone can help. Please..

1.)Suppose there is a tribe named Bugu‐bugu. Also, suppose that the tribesmen can only speak the sounds

“Bu” and “Gu”, wherein uttering “Bu” is as likely as uttering “Gu”. They also name their fellow tribesmen in a very peculiar way: a 4‐long sequence of “Bu”s and “Gu”s (i.e., they can utter “Bugubugu” or “Gubugugububu” but those are not Bugu‐bugu names). Now, the random variable X = longest string of “Bu”s in a Bugu‐bugu tribeman’s name.

a. List the possible names the Bugu‐bugu tribesmen can form with its corresponding X values and construct the PMF of X

b. Find E(X)