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## Homework Statement

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)

## Homework Equations

## 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.