Mathematical Methods · discrete RVs · manipulative

Equally likely outcomes

Uniform means every stick is the same height 1/n. Change n — they stay equal. Load the die — that is no longer uniform.

P(X = x) height 1/n

Outcomes of X

Probability mass function

uniform — each outcome has probability 1/n Σp = 1

Model

6

Sticks are locked equal while the model is uniform. They are not a data histogram.

Show 1/n
dashed equal-height reference

Working

Uniform is a claim about the model (equal probability), not about a sample looking flat.