2023/09/07 by de Assis, Francisco Marcos, de Assis, Juliana Martins, Dias, Micael Andrade
#FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2309.03967
We introduce new method for generating correlated or uncorrelated Bernoulli random variables by using the binary expansion of a continuous random variable with support on the unit interval. We show that when this variable has a symmetric probability density function around 12 , its binary expansion provides equiprobable bits over 0, 1. In addition we prove that when the random variable is uniformly distributed over [0, 1], its binary expansion generates independent Bernoulli random variables. Moreover, we give examples where, by choosing some parameterized nonuniform probability density functions over [0, 1], samples of Bernoulli variables with specific correlation values are generated.