Question: 19. Suppose that liquid in a cubic container is placed in a coordinate system, and at time 0, a pollen particle suspended in the liquid

19. Suppose that liquid in a cubic container is placed in a coordinate system, and at time 0, a pollen particle suspended in the liquid is at (0, 0, 0), the origin. Let Y (t) be the y-coordinate of the position of the pollen after t minutes. Suppose that the process $ Y (t): t ≥ 0 % is a Brownian motion with variance parameter σ2. For 0 < s < t, find E 4 Y (s) | Y (t) = y 5 and Var4 Y (s) | Y (t) = y 5 .

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