Stats Solutions

[Solution Library] Let X_1,...,X_n be i.i.d. observations from a Gamma(1, μ), and Y_1,...,Y_m be i.i.d. observations from a Gamma(1, θ). Also assume

Question: Let \({{X}_{1}},...,{{X}_{n}}\) be i.i.d. observations from a Gamma(1, \(\mu \) ), and \({{Y}_{1}},...,{{Y}_{m}}\) be i.i.d. observations from a Gamma(1, \(\theta \) ). Also assume that X’s are independent of Y’s.

  1. Formulate the Likelihood Ratio Test for testing Ho: \(\mu =\theta \) vs. H1: \(\mu \ne \theta \).
  2. Show that the test in part (a) can be based on the following statistic
\[T=\frac{\sum\limits_{i=1}^{n}{{{X}_{i}}}}{\sum\limits_{i=1}^{n}{{{X}_{i}}}+\sum\limits_{j=1}^{m}{{{Y}_{j}}}}\]

Price: $2.99
Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document


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