I have a distribution X, whose reciprocal Y=1/X is a standard normal distribution Y~N(0,1).

the PDF I achieved for X is 1/(x^2*(2*pi)^0.5)*exp(-1/2*(1/x)^2).

The mean I achieved is 0, by using μ=∫xf(x)dx

I tried to solve variance of X by using σ2=∫x^2f(x)dx, however, something wrong, I can not solve it.

Can somebody help to check my calculations?

Thanks.