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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2016 • Question 6

Question

Math 6010 • Linear Models Spring 2016 • Question 6

Let \(U_0,U_1,\ldots \) be independent and identically distributed random variables, uniform on \([0,1]\). Let \(N\) be a Poisson random variable with \(\mathbb {E}[N]=1\), independent of \(U_0,U_1,\ldots \). Compute \(\mathbb {E}[Y]\), where \(Y=\max _{0\leq k\leq N} U_k\).

Raw LaTeX

Let \(U_0,U_1,\ldots\) be independent and identically distributed
random variables, uniform on \([0,1]\). Let \(N\) be a Poisson random variable with
\(\E[N]=1\), independent of \(U_0,U_1,\ldots\). Compute \(\E[Y]\), where
\(Y=\max_{0\leq k\leq N} U_k\).

Topic Tags

Covariance and Independence Laws of Large Numbers Measure-Theoretic Probability Uniform Integrability and Truncation Methods