 Independent record indicators

ID: independent-record-indicators

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}

E K_{n} = \sum_{i = 1}^{n} 1/ i

and

Var K_{n} = \sum_{i = 1}^{n} (1/ i - 1/ i^{2})

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