This is Q7 page 128 from " Introduction to probability by Joseph K.Blitzstein": Bob is playing a video game that has 7 levels. He starts at level 1,...

This is Q7 page 128 from " Introduction to probability by Joseph K.Blitzstein":

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

p1 of reaching level 2. In general, given that he reaches level j, he has probability pj 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 p1, . . . , p6).:

 PLease solve this problem.