Suppose that you need to generate a random variable Y with a density function f (y) corresponding to a beta distribution with range [0,1], and with a non-integer shape parameter for the beta distribution. For this case there is no closed-form cdf or inverse cdf. Suppose your

choices for generating Y are either:

a) an acceptance-rejection strategy with a constant majorizing function g(u) = V over [0, 1], i.e., generate u1 and u2 IID from a U[0,1] generator and accept y = u1 if Vu2

Or

b) use a numerical approximation to the inverse cdc of Y, say G, generate u from U[0,1]

generator, and let y = G(u).

Discuss the advantages and disadvantages of each approach.