The Opening Scene: Introduction to Applied Statistics

Students often conflate the empirical distribution

\hat{F}_n(x)

with the true population distribution

F(x)

. Remember,

\hat{F}_n(x)

is a step function dependent on the specific sample

\{x_1, \dots, x_n\}

, while

F(x)

is the theoretical, fixed entity we seek to estimate.

Institutional Reference: Applied Statistics