Linear Dependence between Two Bernoulli Random Variables
Linear Dependence between Two Bernoulli Random Variables
The Pearson correlation coefficient, denoted , is a measure of the linear dependence between two random variables, that is, the extent to which a random variable can be written as , for some and some . This Demonstration explores the following question: what correlation coefficients are possible for a random vector , where is a Bernoulli random variable with parameter and is a Bernoulli random variable with parameter ? Interestingly, a two-dimensional Bernoulli random vector has a correlation coefficient that is constrained by the choices of and .
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