Give algorithms for generating random variates with the following densities:
(a) Cauchy
(b) Gumbel (or extreme value)
(c) Logistic
(d) Pareto
For γ = 0 and β = 1 in each of (a), (b), and (c), use your algorithms to generate IID random variates X1, X2, …, X5000 and write out to verify empirically the strong law of large numbers (Sec. 4.6), i.e., that converges to E(Xi) (if it exists); do the same for (d) with c = 1 and α2 = 2.
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