GATE 2023 ST – Question 32

Convergence of Random Variables · Modes of Convergence · 1 mark · Numerical answer

X_n are iid with mean 4 and variance 9. For Y_n=(X₁+⋯+X_n)/n,find lim as n→∞ of E[((Y_n−4)/√n)²],as an integer.

Show answer and explanation

Correct answer: 0 to 0

Explanation

E Y_n=4 and Var Y_n=9/n. The requested expectation is Var(Y_n)/n=9/n²,whose limit is **0**. The division by √n is part of the printed expression.

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