Cold calls until the first meeting (geometric)

Question

Each cold call independently books a meeting with probability p = 0.2. Let N be the number of calls up to and including the first meeting. What are the mean and variance of N?

Accepted Answer

Counting trials until the first success, with the success trial included, is a geometric distribution. Its formulas: - Mean = 1/p. If one in five calls works, you expect to make 5 calls to get one meeting. - Variance = (1-p)/p^2. Plug in p = 0.2: \mathbb{E}[N] = \frac{1}{0.2} = 5, \qquad \operatorname{Var}(N) = \frac{0.8}{0.2^2} = \frac{0.8}{0.04} = 20. Standard deviation \sqrt{20} \approx 4.47: the count is quite variable, because occasionally you hit a long dry streak. That long right tail is the signature of the geometric. Takeaway. Trials until the first success average 1/p = 5 with varia…

Cold calls until the first meeting (geometric)

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