a fair die is tossed n times
let X be the number of times that the pattern 1 2 is observed
(a) E(X) (b) VAR(X)
(it's a question from a past exam)
The Attempt at a Solution
E(X)=E(E(X|first=1)+E(X|first ≠ 1))
I think I'm setting up the equation wrong since I got something other than 12/(6^3) as I plug in n=3.
However, even if I set it up correctly, I still have no idea how to solve this equation....
Any help would be greatly appreciated.