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]

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dist = TransformedDistribution[u + v,
{u \[Distributed] NormalDistribution[μ1, σ1],
v \[Distributed] NormalDistribution[μ2, σ2]}];
PDF[dist, x]


Note: check the correct syntax for PDF in the docs.

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Thanks that works! –  Matt Asher Mar 13 '13 at 17:56
@Matt, my pleasure. Welcome to Mathematica.SE. –  kglr Mar 13 '13 at 18:02
Thanks for the welcome! I do most of my coding in R, working on a review of Mathematica for R users right now... –  Matt Asher Mar 13 '13 at 18:12
@MattAsher I suppose you're aware of Mathematica 9's new RLink feature, right? –  Sjoerd C. de Vries Mar 13 '13 at 19:58
@Sjoerd C. de Vries Yes I am. I'll be evaluating some of RLink's capabilities in my review. –  Matt Asher Mar 15 '13 at 16:40