MathDB
Miklos Schweitzer 1964_10

Source:

September 20, 2008
integrationprobability and stats

Problem Statement

Let ε1,ε2,...,ε2n \varepsilon_1,\varepsilon_2,...,\varepsilon_{2n} be independent random variables such that P(\varepsilon_i\equal{}1)\equal{}P(\varepsilon_i\equal{}\minus{}1)\equal{}\frac 12 for all i i, and define S_k\equal{}\sum_{i\equal{}1}^k \varepsilon_i, \;1\leq k \leq 2n. Let N2n N_{2n} denote the number of integers k∈[2,2n] k\in [2,2n] such that either Sk>0 S_k>0, or S_k\equal{}0 and S_{k\minus{}1}>0. Compute the variance of N2n N_{2n}.
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