Bob is playing a video game that has 7 levels. He starts at level 1, and has a probability p1 of reaching level 2.


Bob is playing a video game that has 7 levels. He starts at level 1, and has a probability $p_1$ of reaching level 2. In general, given that he reaches level j, he has probability $p_j$ of reaching level j + 1, for 1 ≤ j ≤ 6. Let X be the highest level that he reaches. Find the PMF of X (in terms of $p_1$,··· ,$p_6$).

  • We did not have time to go over this section in class because we ran out of time. I was thinking the PMF could be P(X=x)=($p_1$)($p_2$)…($p_{x-1}$). I am extremely confused, any help would really be appreciated.