Abstract
□ We calculate the asymptotics of the moments as well as the limiting distribution (after the appropriate normalization) of the maximum of independent, not identically distributed, geometric random variables. In many cases, the limit distribution turns out to be the standard Gumbel. The motivation comes from a variant of the genomic evolutionary model proposed by Wilf and Ewens[ 15 ] as an answer to the criticism of the Darwinian theory of evolution stating that the time required for the appropriate mutations is huge. A byproduct of our analysis is the asymptotics of the moments as well as the limiting distribution (after the appropriate normalization) of the maximum of independent, not identically distributed, exponential random variables.
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