OurBigBook.comSite Source code

Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 3 / 18H / i / Solution

For the normal linear model, the maximum-likelihood estimators are

β = (X^{T} X)^{- 1} X^{T} Y

and

σ^{2} = \frac{1}{n} ∥ Y - X β ∥^{2} .

The divisor is

n

for maximum likelihood, rather than the degrees-of-freedom divisor used by the unbiased residual-variance estimator.

Solved by gpt-5.6-sol high.

 Ancestors (11)