The random classifier $($RC$)$ gives the predictions

$[$

$0\mathrm{.}5$

$,$

$0\mathrm{.}5$

$,$

$0\mathrm{.}5$

$,$

$0\mathrm{.}5$

$]$

$[0\mathrm{.}5,0\mathrm{.}5,0\mathrm{.}5,0\mathrm{.}5].$

For this sample and according to the BCE loss, does the logistic regression $($LR$)$ performs better than the random classifier?