Variance of product of two normal distributions

1. What is the distribution of the product of two normal distributions?
2. Is the product of two normal distributions normal?
3. How to find standard deviation of a product of two random variables?
4. What is the variance of a product?

What is the distribution of the product of two normal distributions?

The product of two normal PDFs is proportional to a normal PDF. This is well known in Bayesian statistics because a normal likelihood times a normal prior gives a normal posterior. But because Bayesian applications don't usually need to know the proportionality constant, it's a little hard to find.

Is the product of two normal distributions normal?

It is clear the product of normal distributed variables is not normal distributed.

How to find standard deviation of a product of two random variables?

Sum: For any two independent random variables X and Y, if S = X + Y, the variance of S is SD^2= (X+Y)^2 . To find the standard deviation, take the square root of the variance formula: SD = sqrt(SDX^2 + SDY^2).

What is the variance of a product?

Product variance, otherwise known as loss or shrinkage, is one of the biggest detractors from a beverage program's profitability. It represents the difference between the amount of product sold over a given period of time, and the amount of product used over that same period.