Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2013 • Question 3

Question

Math 6010 • Linear Models Fall 2013 • Question 3

Suppose \(X_1,X_2,\ldots ,X_n\) are i.i.d. random variables, and \(1\leq X_1\leq 2\) a.s. Compute, for every \(1\leq i\leq j\leq n\), the quantity \[ \mathbb {E}\left (\frac {X_i+\cdots +X_j}{X_1+\cdots +X_n}\right ). \]

Raw LaTeX

Suppose \(X_1,X_2,\ldots,X_n\) are i.i.d. random variables, and
\(1\leq X_1\leq2\) a.s. Compute, for every \(1\leq i\leq j\leq n\), the quantity
\[
  \E\left(\frac{X_i+\cdots+X_j}{X_1+\cdots+X_n}\right).
\]

Topic Tags

Convergence in Probability and Almost Sure Convergence Laws of Large Numbers Measure-Theoretic Probability Uniform Integrability and Truncation Methods