GATE 2026 ST – Question 31

Stochastic Processes · Brownian Motion · 1 mark · Numerical answer

For standard Brownian motion W, let Z₁=W(1)+W(2),Z₂=W(2)+W(3). If ρ is their correlation, find 10ρ to two decimals.

Show answer and explanation

Correct answer: 8.91 to 8.97

Explanation

Use Cov(W(s),W(t))=min(s,t). Var Z₁=1+2+2=5, Var Z₂=2+3+4=9, and covariance=1+1+2+2=6. Thus 10ρ=60/√45≈**8.94**.

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