Hi all im having some simple problems in brownian motion at the moment. I have done one question below and just want to verify whether or not it is the right answer if not then please recorrect me.

the other im just out of ideas in solving it. If you could help me, your assitance is much appreciated! Thank you!

$\displaystyle V_t = 2B_t + 3t$

The covarance of $\displaystyle V_t$ is 21t. Is that the right answer?

My second quesiton is:

Let $\displaystyle B_1(t)$ and $\displaystyle B_2(t)$ be independent Brownian motions and defined:

$\displaystyle W(t) = \frac{1}{\sqrt{2}}(B_1(t) + B_2(t))$

Show that $\displaystyle W(t)$ is a brownian motion.

If possible can you show that they have independent increments, Gaussian increments and has a continuity path.

Thanks again!