[Solved] STAT5113 Homework1

A1: Find the MLE of the unknown parameter (0,1) based on one observation of X Bin(n,). Are there particular values of the data x for which the MLE does not exist?

A2: Find the MLE of the unknown positive parameter from a random sample of size n from the continuous uniform distribution on [0,].

A3: Consider independent random variables with:

X_i N(₁,²), i = 1,,n₁, Y_j N(₂,²), j = 1,,n₂,

Formulate the statistical model and derive the MLE of the unknown parameters.

A4: The Lognormal distribution is sometimes used to model positive quantities and it has density

Compute MLEs of and based on the leukemia survival data described in class. Compare the fit of the Lognormal model with that of the Gamma and Weibull models: which model appears to give the best fit for the survival data?

B1: Consider a random sample from the family of distributions defined by the pdf

where x₀ is a known positive value ans is an unknown positive parameter. Find the MLE of .

B2: In R, get hold of the speed-of-light measurements by typing: sp = morley[[Speed]]. Use the method of maximum likelihood to fit both a normal and a Gamma model to the data. Which model gives the best fit?