Independent record indicators ($Y_i\sim \mathrm{Bernoulli}(1/i)$)

The indicators $Y_i=1_{\{R_i=1\}}$ 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 $K_n={\sum }_{i=1}^n{Y}_i$, expectation and variance additivity for independent random variables give $E{K}_n={\sum }_{i=1}^{n}1/i$ and $\mathrm{Var}{K}_n={\sum }_{i=1}^n(1/i-1/i^2)$.