Mean and variance of a Brownian motion process

Question

Say $X(t),t\geq 0,$ denotes a Brownian motion process with drift parameter $\mu=3$ and variance parameter $\sigma^2 = 9$. If $X(0)=10$ I want to find

1. $E[X(2)]$
2. $Var[X(2)]$
3. $P(X(2)>20)$

My reasoning is the following: Since the Brownian motion has a Gaussian probability density with mean $t\mu$ and variance $t\sigma^2$, I would say that

1. $E[X(2)] = 2\times 3 = 6$
2. $Var[X(2)] = 2\times 9 = 18$
3. $P(X(2)>20) = \int_{20}^\infty{\frac{1}{6\sqrt{2\pi}}e^{-(x-6)^2/36}dx}$

Is my reasoning correct?