notation of distribution I have a question: 

Does  $$N(0, x)$$ mean a normal distribution with mean $0$ and variance $x$? Or standard deviation $x$?

The notation seems ambiguous sometimes.
 A: Some people use $N(0,x)$ to denote the normal with SD $x$, some with variance $x$. This depends on the author, so you should look for the first place where the paper or book that you're reading uses this notation; they should define it there.
A: This question came up on stats.SE as well.  Apparently, there
are three different conventions in use in the statistical 
literature, and for $x$ in $N(0,x)$ to mean standard deviation $\sigma$
is quite common (I am told Wolfram Alpha uses this convention,
to answer a question from @MichaelHardy).  What is more interesting
is a comment on this question
on Stats.SE which says that $x$ can even mean $1/\sigma^2$ in
Bayesian contexts. 
This answer summarizes
the discussion on stats.SE.
A: You are right, it might be confusing, though for 1-dimensional case only.
In general, for $n$-dimensional normal distribution you have $$X\sim\mathcal{N}\left(\mu,\Sigma\right)$$ where $\Sigma$ is the covariance matrix defined as $$\Sigma_{ij}=\operatorname{Cov}\left(X_i,X_j\right)$$ which is simply $\operatorname{Var}(X_i)$ when $i=j$. So, for 1-dimensional case it is just the variance. I believe this way it is easier to remember.
