I would want to ask if I have a random variable $A \sim N(b,c)$ then what is the distribution of the inverse of $A$?
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As stated in wikipedia and this math.stackexchange question, $1 / A$ has a bimodal distribution.
However, the mean and the variance and higher order moments of $1 / A$ are not defined (as shown here for the mean).
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$\begingroup$ Surely you mean bimodal and not binomial $\endgroup$– yokiCommented Nov 23, 2015 at 21:20
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1$\begingroup$ (+1) Wikipedia asserts bimodality only for the case $b=0$ and $c=1$. Clearly the value of $c$ will not affect this characteristic, but in principle $b$ can. Nevertheless, $1/A$ will always be bimodal, because it has a density of $0$ at $0$ and both the positive and negative parts are unimodal (as becomes obvious when you consider the distribution of their logarithms). $\endgroup$– whuber ♦Commented Nov 23, 2015 at 21:46