Thread: Exponential of square of Normal Distribution

Dear All, I come across an equation when reading a paper. The author has skipped the steps to derive the equation. I am new to distributions. Could you please help me look into it? Thanks in advance!

y~N(0,1+e/e)

I cannot read the exponent on the right in front of the integral.
But from what I can see, this does not make sense.
On the RHS, y is a dummy variable of integration, but it's a variable on the LHS.

Thank matheagle for your reply. My question can be simplified as following:

Given x~N(0,1) , a standard normal variable.
What is the expectation of exp(-x^2)?

Thanks in advance!

Just combine the exponentials and create a new normal rv.
There's no reason to integrate.

we know that

you want

Thank matheagle.
I got it!