Distance of the particle from origin after t units of time

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Question: Suppose that liquid in a cubic container is placed in a coordinate system. Suppose that at time 0, a particle is at (0, 0, 0), the origin. Let ! X(t), Y (t), Z(t)" be the coordinates of the particle after t units of time, and assume that X(t), Y (t), and Z(t) are independent Brownian motions, each with variance parameter σ2. Let D(t) be the distance of the particle from the origin after t units of time. Find E 4 D(t)5.

Reference no: EM131812203

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