Write W₄=W₂+(W₄−W₂). The increment is independent of W₂,has mean zero and variance 2. Conditional mean is 2 and conditional variance 2,so the second moment is 2²+2=**6**.
More Brownian Motion questions
GATE 2022 ST Q24– B(t) is standard Brownian motion. If P[B(2)+2B(3)>1]=1−Φ(1/√α),α>0,find α as an integer.
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