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.