Likelihood is the product of probability distributions
Likelihood \( \neq \) Probability
\[ L(\theta) = \prod_{i=1}^n f(x_i; \theta) \]
\[ L(\theta) = f(x_1; \theta) \cdot f(x_2; \theta) \cdot \ldots \cdot f(x_n; \theta) \]
\( f(x_i; \theta) \): parametric probability distribution
\[ \log L(\theta) = \sum_{i=1}^n \log f(x_i; \theta) \]