# MLE

Verify that ?(^) maximizes the likelihood function L(?; y) if and only if it also maximizes the log of the likelihood function, InL(?; y). That is, prove that

L(?(^); y)>L(?(~);y) if and only if lnL(?(^);y)>lnL(?(~);;y)for all ?(~);??(^)

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Verify that θ(^) maximizes the likelihood function L(θ; y) if and only if it also maximizes the log of the likelihood function, InL(θ; y). ...

#### Solution Summary

Verify that ?(^) maximizes the likelihood function L(?; y) if and only if it also maximizes the log of the likelihood function, InL(?; y). That is, prove that

L(?(^); y)>L(?(~);y) if and only if lnL(?(^);y)>lnL(?(~);;y)for all ?(~);??(^)

$2.19