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Consider the target p.d.f. f(x) =((3/14)(1 + x2), 0 ≤ x ≤ 2, 0, otherwise. (a) Express f(x) as a mixture p1g1(x)+p2g2(x) where p1,p2 > 0 and p1 + p2 = 1, and where both g1(x) and g2(x) are p.d.f.s. (b) Using part (a), write down an algorithm for generating X ∼ f by the composition method expressing your results in terms of i.i.d. U1,U2 ∼ U[0,1].
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