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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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  • Surely you mean bimodal and not binomial – yoki Nov 23 '15 at 21:20
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    (+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). – whuber Nov 23 '15 at 21:46