Let $\{X_k:k\geq0\}$ a Standard Brownian motion. Compute the following propability
$$P(X_2>0|X_1>0).$$
The question is: Are $\{X_2\}$ and $\{X_1\}$ independent?
I know:
$$P(X_2>0|X_1>0)=\frac{P(X_2>0\ \cap X_1>0)}{P(X_1>0)}$$ and if I assume that $X_1$ and $X_2$ are independent, then I have to show that $$P(X_2>0|X_1>0)=P(X_2>0).$$
How can I calculate it?