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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2008 • Question 10

Question

Math 6010 • Linear Models Spring 2008 • Question 10

Show that the number of fixed points in a random permutation of length \(n\) is asymptotically Poisson with mean 1. Hint: Use characteristic functions. Write \(e^{it1_A}\) as \(1+(e^{it}-1)1_A\).

Raw LaTeX

Show that the number of fixed points in a random permutation of
length \(n\) is asymptotically Poisson with mean 1. Hint: Use characteristic
functions. Write \(e^{it1_A}\) as \(1+(e^{it}-1)1_A\).

Topic Tags

Characteristic Functions and Fourier Inversion Measure-Theoretic Probability Uniform Integrability and Truncation Methods