# What is the pdf of Y and what are the mean and variance?

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#### pmonon

##### Full Member level 3
I am concerned with a r.v. Y=X ^ -1 where X ~ N(0,1). What is the pdf of Y and what is the mean, variance? Any one, please?

#### eternal_nan

##### Full Member level 3
complicated pdf?

Mean is calculated by substituting x*pdf(x) in the interval to f(x)*pdf(x); similar approach for the variance: just substitute the RV index with the function on the RV index.

### pmonon

Points: 2

#### pmonon

##### Full Member level 3
Re: complicated pdf?

eternal_nan said:
Mean is calculated by substituting x*pdf(x) in the interval to f(x)*pdf(x); similar approach for the variance: just substitute the RV index with the function on the RV index.

But when you evaluate the integral for mean what happens? Is it zero or infinity or undefined? Can you try that for me?

#### eternal_nan

##### Full Member level 3
complicated pdf?

Sorry pmonon, the mechanics of evaluating integrals was never my stronger side. Anyhow, N(0,1) means normal distribution or uniform distribution for the original RV?

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