Recitation 2 Here' s an informal explanation The probability that stencil falls from the cliff of Doom on the k-th step is approximately 1/k-3/2. Thus, the probability that he falls eventually is Pr(falls off cliff)2 k3/2 You can verify by integration that this sum converges. The exact sum actually con erges to 1. On the other hand, the expected time until he falls is Ex(hops until fall)a>k √k And you can verify by integration that this sum diverges. So our answers are com patibleRecitation 23 6 Here’s an informal explanation. The probability that Stencil falls from the Cliff of Doom on the k­th step is approximately 1/k3/2 . Thus, the probability that he falls eventually is: � 1 ∞ Pr (falls off cliff) ≈ k3/2 k=1 You can verify by integration that this sum converges. The exact sum actually con￾verges to 1. On the other hand, the expected time until he falls is: �∞ ∞ 1 � 1 Ex (hops until fall) ≈ k · = k3/2 √ k k=1 k=1 And you can verify by integration that this sum diverges. So our answers are com￾patible!