Brownian motion and covariance
Solution 1:
In your proof you use the fact that $B_s$ is independent of $B_t-B_s$ (indepedent increments) but this is only true if $s\leq t$.
In your proof you use the fact that $B_s$ is independent of $B_t-B_s$ (indepedent increments) but this is only true if $s\leq t$.