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GATE 2021 ST – Question 12

Stochastic Processes · Brownian Motion · 1 mark · Multiple choice

For standard Brownian motion W(t),find Var[W(1)W(2)].

  1. 1
  2. 2
  3. 3
  4. 4

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Show answer and explanation

Correct answer: (C) 3

Explanation

Write W₂=W₁+Z,where W₁,Z are independent N(0,1). The product is W₁²+W₁Z. Its mean is 1,and second moment is E W₁⁴+E W₁²E Z²=3+1=4. Variance=4−1=**3, C**.

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