In reply to Andy Wheeler.

Thanks for writing. The support of a function, f, is often defined as the domain for which the function is nonzero: {x|f(x)^=0}. Depending on the parameters, the PDF of Beta distribution either has support (0,1), [0,1). (0,1], or [0,1]. In probability theory, the support of a DISTRIBUTION is always the closure of the support of the PDF, so the support of the beta distribution is [0,1].