Independence of two events in a Brownian motion

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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?