So this is an exam question I had recently and I honestly had no idea on how to solve it.

Let W(t) be a Brownian Motion stochastic process at time t with drift p and variance v^2

Let s exist such that t1 < s < t2.

  1. Find E[W(s)| W(t1) = a, W(t2) = b]
  2. Find Var[W(s)| W(t1) = a, W(t2) = b]

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