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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2009 • Question 2

Question

Math 6010 • Linear Models Spring 2009 • Question 2

(a) Find a closed-form expression (i.e., one with no summation sign) for \(\mathbb {E}[(X+1)^{-1}]\) when \(X\) is binomial\((n,p)\) with \(n\geq 1\) and \(0<p<1\).

(b) Find a closed-form expression for \(\mathbb {E}[(X+1)^{-1}]\) when \(X\) is Poisson\((\lambda )\) with \(\lambda >0\). You may use the result of part (a) here.

Raw LaTeX

\textbf{(a)} Find a closed-form expression (i.e., one with no
summation sign) for \(\E[(X+1)^{-1}]\) when \(X\) is binomial\((n,p)\) with \(n\geq1\)
and \(0<p<1\).

\textbf{(b)} Find a closed-form expression for \(\E[(X+1)^{-1}]\) when \(X\) is
Poisson\((\lambda)\) with \(\lambda>0\). You may use the result of part (a) here.

Topic Tags

Measure-Theoretic Probability Uniform Integrability and Truncation Methods