This Machine Learning course with timestamp is talking about PERFORMANCE MEASURE.
Assume there are 3 loan officers A, B and C (correspond to you, blank, your "Friend" on the blackboard) , assigned the probabilities (predictions) of default to 2 loans.
the column on the rightmost is the actual outcomes of loans, namely, not default and default.
the column on the leftmost is predictions made by A, 0.2 chance of default for both loans.
B's predictions are 0.1 and 0.5
C predicted 0.3 chance of default for both loans.
the bottom is the likelihood that A's estimates applied to the actual complete set of outcomes, according to A, which is 0.8*0.2, why is that?
wiki gives this formulas to calculate the likelihood for Discrete probability distribution
${\displaystyle {\mathcal {L}}(\theta \mid x)=p_{\theta }(x)=P_{\theta }(X=x),}$
question
wiki's formula put observed data at the right of the bar symbol $\mid$, which means
over the outcome x, not over the parameter $\theta$
while that lecturer put "Me" at the right of the bar symbol $\mid$, which is implying
over the parameter $\theta$, not over the outcome x.
which is a opposite meaning.
What am I missing?