Independent record indicators
= Independent record indicators
{title2=$Y_i\sim\operatorname{Bernoulli}(1/i)$}
The indicators $Y_i=\mathbf1_{\{R_i=1\}}$ of successively smaller records are <independent> and have <Bernoulli distributions> of parameters $1/i$. Successively larger records use $R_i=i$ and have the same laws. For $K_n=\sum_{i=1}^nY_i$, <expectation> and <variance additivity for independent random variables> give $E K_n=\sum_{i=1}^n1/i$ and $\operatorname{Var}K_n=\sum_{i=1}^n(1/i-1/i^2)$.