When you apply a Gaussian probability densityfunction to Rectified Linear/Sigmoid function,
you will get a rectified(*)/distorted Gaussian function.
(*)rectified Gaussian function is a mixture of delta and truncated gaussian as shown belown
I am wondering, what is the Expectation and Variance of this rectified/distorted Gaussian?
The Expectation of distorted Gaussian from Sigmoid is shown below.
Expected value of applying the sigmoid function to a normal distribution
How about Variance? or Expectation and Variance of rectified Gaussian from Rectified Linear?