m*****r
发帖数: 84 | 1 It took a while to come up the following solution.Yep, it should be a PHD
qualify题目.
Let X be number of tosses. Let q = 1-p
First, if p = 1, then, clearly E(X) = m.
Suppose 0 < p < 1. We can calculate the expectation E(X) via conditioning
Let t_i be the result of the i-th toss
Consider using telescoping by observing that
E(X) = E(X|t_1 = H)p + (E(X)+1)q
E(X|t_1 = H) = E(X|t_1 = H,t_2 = H)p + (E(X)+2)q
E(X|t_1 = H,t_2 = H) = ... 阅读全帖 |
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