HI, i'm struggling with a question on maximum likelihood and lookin for help here it is:

Let x1, x2, . . . , xn be an iid sample from a probability density with

parameter θ.

(a) Show that the value that maximizes the log-likelihood also maxi-

mizes the likelihood. [7]

Hint: This does not require extensive calculations. Remember

that the log() function is increasing

(b) Suppose that ϕ = g(θ) where g is a one-to-one function that is

dierentiable. Show that that the maximum likelihood estimate

for ϕ is g(^θ).

Hint 1: Look at a specic example rst. For example, if the data

are Poisson(θ) distributed and ϕ = log(θ). In this case, you can

check directly.

Hint 2: Don't forget about the chain rule for diffrentiation