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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2018 • Question 5

Question

Math 6010 • Linear Models Spring 2018 • Question 5

Prove or disprove the following statement. If \(X_n\) converges weakly to \(X\) as \(n\to \infty \) and \(Z_n-X_n\) converges weakly to 0 as \(n\to \infty \), then \(Z_n\) converges weakly to \(X\) as \(n\to \infty \).

Raw LaTeX

Prove or disprove the following statement. If \(X_n\) converges
weakly to \(X\) as \(n\to\infty\) and \(Z_n-X_n\) converges weakly to 0 as
\(n\to\infty\), then \(Z_n\) converges weakly to \(X\) as \(n\to\infty\).

Topic Tags

Uniform Integrability and Truncation Methods Weak Convergence and Distributional Limits