I am aware that the sum of two (or more) normally distributed Random Variables is not necessarily also normal.
I do have questions regarding the special case where I have the following addition:
For c $\in \mathbb R$, is c + N(0,a), where I add a normal Random Variable with mean zero and variance a to c, is then the sum normally distributed? Also, does this addition correspond to drawing a random variable X too from a Normal distribution with mean and then add it to N(0,a)?
Hope the question is clear, thanks