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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Summer 2020 • Question 10

Question

Math 6010 • Linear Models Summer 2020 • Question 10

Let \(X_1,\ldots ,X_n\) be independent and identically distributed random variables with (unknown) density function \(F\). Let \[ F_0(t)=(1-e^{-t})1\{t>0\}. \] We wish to test \(F(t)=F_0(t)\) for all \(t\). Explain the application of the \(\chi ^2\) goodness-of-fit test.

Raw LaTeX

Let \(X_1,\ldots,X_n\) be independent and identically distributed
random variables with (unknown) density function \(F\). Let
\[
  F_0(t)=(1-e^{-t})1\{t>0\}.
\]
We wish to test \(F(t)=F_0(t)\) for all \(t\). Explain the application of the
\(\chi^2\) goodness-of-fit test.

Topic Tags

Covariance and Independence F-Tests and t-Tests Quadratic Forms and Chi-Squared Distributions Uniform Integrability and Truncation Methods