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I offer the following based on Monte Carlo integration, but trying to make use of the facilities Mathematica provides: weights = {2/3, 1/3}; means = {-3, 2}; sd = Sqrt[2]; distributions = NormalDistribution[#, sd] & /@ means; fdist = MixtureDistribution[weights, distributions]; qdist1 = TransformedDistribution[Log[PDF[fdist, f]], Distributed[f, ...



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