# Closed form for convolutions of random variables

Is it possible to get Mathematica (9) to calculate PDF's for combined distributions? I can't seem to find the right notation, if this is possible at all. My attempts:

PDF[NormalDistribution[0, 1] + NormalDistribution[0, 1], x]


Nor can we store a distribution to a variable:

z \[Distributed] NormalDistribution[0, 1]
PDF[z, x]


dist = TransformedDistribution[u + v,