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This is n choose \frac{1}{2}(n+k) Appreciate your comments.

Let Pr(X_{i} = +1) =\frac{2}{3} = 1 - Pr(X_{i} = -1) , and S_{n} = \sum{X_{i}}, For each k≥1, define T_{k}\ =\ min \left\{n≥1: S_{n} = k \right\}. Calculate E[T_k], and Var[T_k]. 2. Homework Equations E[T_k] = \sum_{n=1}^{n=∞}{n Pr(T_k = n)} , and E[T_k]^2 = \sum_{n=1}^{n=∞}{n^2 Pr(T_k...