  Randomized libraries are increasingly popular in protein engineering and
other biomedical research fields. Statistics of the libraries are useful to
guide and evaluate randomized library construction. Previous works only give
the mean of the number of unique sequences in the library, and they can only
handle equal molar ratio of the four nucleotides at a small number of mutation
sites. We derive formulas to calculate the mean and variance of the number of
unique sequences in libraries generated by cassette mutagenesis with mixtures
of arbitrary nucleotide ratios. Computer program was developed which utilizes
arbitrary numerical precision software package to calculate the statistics of
large libraries. The statistics of library with mutations in more than $20$
amino acids can be calculated easily. Results show that the nucleotide ratios
have significant effects on these statistics. The more skewed the ratio, the
larger the library size is needed to obtain the same expected number of unique
sequences. The program is freely available at
\url{http://graphics.med.yale.edu/cgi-bin/lib_comp.pl}.
