GATE 2022 ST – Question 24

Stochastic Processes · Brownian Motion · 1 mark · Numerical answer

B(t) is standard Brownian motion. If P[B(2)+2B(3)>1]=1−Φ(1/√α),α>0,find α as an integer.

Show answer and explanation

Correct answer: 22 to 22

Explanation

The linear combination is centered normal. Its variance is Var B₂+4Var B₃+4Cov(B₂,B₃)=2+12+4·2=22. Standardization gives α=**22**.

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