Give algorithms for generating random variates with the following densities:(a) Cauchy(b)...

Give algorithms for generating random variates with the following densities:

(a) Cauchy

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(b) Gumbel (or extreme value)

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(c) Logistic

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(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(X_i) (if it exists); do the same for (d) with c = 1 and α₂ = 2.