Let each individual observation, Yi be an independent sample from a Gaussian distribution with mean η and variance, σ2, i.e., Yi ∼ N (η(x, θ), σ2 ; i = 1, 2,. .., n; i i where the variances are not necessarily equal.

(i) Determine the maximum likelihood estimate of the parameter θ in the one- parameter model, η = θx and show that it has the form of a weighted least squares estimate. What are the weights?

(ii) Determine the maximum likelihood estimates of the parameters θ0 and θ1 in the two-parameter model, η = θ0 + θ1x Show that these are also similar to weighted least squares estimates. What are the weights in this case?