GATE 2022 ST – Question 32

Stochastic Processes · Poisson and Birth-Death Processes · 1 mark · Numerical answer

X(t) is a Poisson process with P(X(t)=n)=e^(−4t)(4t)^n/n!. If C(t₁,t₂) is its covariance function,find C(5,3),as an integer.

Show answer and explanation

Correct answer: 12 to 12

Explanation

The rate is 4. Write X(5)=X(3)+[X(5)−X(3)],with an independent increment. Therefore Cov(X₅,X₃)=Var X₃=4·3=**12**.

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