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when f is the Student’s t(5) distribution density. In our book, we compare a few importance sampling solutions, but it seems someone (the instructor?) suggested to this X’idated reader to use a mixture importance density

with

and

i.e. with a Cauchy and a power component. The suggested solution in our book is a folded Gamma distribution

The above graph is my final answer to this X’idated reader (after several exchanges in the comments), comparing the three solutions in terms of variability. I used

for the third box. The gradual improvement brought by importance sampling is clear there. Which makes me think we should present the comparison that way in the next edition of Monte Carlo Statistical Methods.