This paper describes techniques for constructing statistically indepen
dent binary sequences with prescribed ratios of zeros and ones. The fi
rst construction is a general recursive construction, which forms the
sequences from a class of ''elementary'' sequences. The second constru
ction is a special construction which can be used when the ratio of on
es to zeros is expressed in binary notation. The second construction i
s shown to be optimal in terms of the numbers of input sequences requi
red to construct the desired sequence. The paper concludes with a disc
ussion of how to generate independent ''elementary'' sequences using s
imple digital techniques.