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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2014 • Question 3

Question

Math 6010 • Linear Models Fall 2014 • Question 3

Suppose \(X=\operatorname {Poisson}(\lambda )\) for some \(\lambda >0\). Prove that \(\mathbb {P}\{X>e\lambda \}\leq e^{-\lambda }\).

Raw LaTeX

Suppose \(X=\operatorname{Poisson}(\lambda)\) for some \(\lambda>0\).
Prove that \(\Prob\{X>e\lambda\}\leq e^{-\lambda}\).

Topic Tags

Measure-Theoretic Probability Uniform Integrability and Truncation Methods