How can variance and mean of brownian motion be stated I have seen in the construction of brownian motion that the Its mean is 0 and variance t. i.e
$E(B(t))=0$ , $Var(B(t))=t$ Why in a problem sheet does it state $B_{j}(t)$ for $j=1,...,n$ are brownian motions with variances $\sigma^{2}_{j}$. How can these be brownian motion  with these variances... is it saying $Var(B_{j}(t)) \neq t$

We usually denote by $\sigma^2$ the volatility of a brownian motion, not its variance, which is $\sigma^2 \times t$. It might help you to understand.
