If X is normal and centered around 0, then the average of 1/X does not exist (math speak for "is infinity" in this case). In these cases Monte Carlo simulations

If X is normal and centered around 0, then the average of 1/X does not exist (math speak for "is infinity" in this case). In these cases Monte Carlo simulations are not reliable because they give high variance estimates (math speak for "the histogram varies run by run"). The actual distribution of 1/X is fairly interesting, see https://en.m.wikipedia.org/wiki/Inverse_distribution#Reciprocal_normal_distribution https://en.m.wikipedia.org/wiki/Inverse_distribution#Recipro...