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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2011 • Question 6

Question

Math 6010 • Linear Models Spring 2011 • Question 6

(a) Let \(X\) be a random variable with characteristic function \(\varphi \). Show that \(X\) is symmetric if and only if \(\varphi (t)\) is real for all \(t\).

(b) Give three distinct examples of real characteristic functions.

Raw LaTeX

\textbf{(a)} Let \(X\) be a random variable with characteristic
function \(\varphi\). Show that \(X\) is symmetric if and only if \(\varphi(t)\) is
real for all \(t\).

\textbf{(b)} Give three distinct examples of real characteristic functions.

Topic Tags

Characteristic Functions and Fourier Inversion Probability Inequalities and Tail Bounds Symmetric Matrices Uniform Integrability and Truncation Methods