In many instances the Metropolis Algorithm is the algorithm of choice because either (i) there are no obvious candidate densities that satisfy the Accept/Reject supremum condition, or (ii) the supremum condition is difficult to verify, or (iii) laziness leads us to substitute computing power for brain power.
For each of the following situations show how to implement the Metropolis Algorithm to generate a sample of size 100 from the specified distribution.
(a) X ~ 1/σ f[(x - μ), /σ] f = Student's t with v degrees of freedom, v, μ, and a known
(b) X ~ lognormal(μ, σ2), μ, σ2 known
(c) X ~ Weibull(