Assume $\{B_t:t\ge0\}$ be a brownian motion process. Is $B_s-\frac{s}{t}B_t$ and $B_t$ independent given that ($s\le t$)
2026-04-23 20:31:06.1776976266
Are these 2 random variable independent???
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Hint: The random vector $(B_s-(s/t)B_t,B_t)$ is centered normal. There is a simple way to check that some entries of a normal vector are independent, you could try it.