Independent tosses of a loaded die with probabilities $p_i$ , $i$ = 1, ..., 6, are performed.
- Let N denote the number of tosses until the initial outcome has occurred exactly 3 times. For instance, if the toss results are 4,3,4,5,1,6,2,4 then N = 8. Find E(N).
- Find the expected number of tosses needed until both 1 and 6 appeared. Compute it when the die is fair.