We estimate the logistic regression coefficient vector β by minimizing J(β)= (-log) likelihood function. Which three of

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We estimate the logistic regression coefficient
vector β by
minimizing J(β)= (-log) likelihood
function. Which three of the following
statements about this cost
function J(β) are correct?
-The MLE of β, i.e., the minimizer
of J(β), may not exist.
-The cost function J(β) for logistic
regression is only positive at some β values,
e.g., at the MLE of β.
-The cost function J(β) for logistic
regression is convex, so any local minimum is a global minimum.
-The cost function J(β) for logistic
regression is always non-negative.
-The Newton-Raphson algorithm, which we use to find the
minimizer of J(β), could get stuck at a
local minimum, even if the global minimum exists.