1. The problem statement, all variables and given/known data 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) 2. Relevant equations 3. The attempt at a solution E(X)=E(E(X|first=1)+E(X|first ≠ 1)) let E(X)=f(n) f(n)=((1+f(n-2))*(1/6)+(5/6)*f(n-1))*(1/6)+f(n-1)*(5/6) 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.