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David is playing a PS4 game that has 5 levels. He starts at level 1, and...

David is playing a PS4 game that has 5 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 the next level j + 1, for 1 ≤ j ≤ 4. Let X be the highest level that David reaches. Find the PMF of X (in terms of p1, ..., p4).

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