Section 2 · Lecture 05 · Intro to Probability

Two Dice

All 36 outcomes of rolling two dice are equally likely, but the random variable built from them isn't. Click a value of Y to see why.

The setup, in notation

Three different spaces, and the rule that connects them.

Outcome space, O {(1,1), (1,2), …, (6,6)} — 36 equally likely pairs

Random variable, Y Y(i, j) = i + j — a rule assigning a number to every outcome

Measurement space {2, 3, …, 12} — the possible values Y can take

Outcome space O

Every cell is one outcome (die 1, die 2). The number shown is Y applied to that outcome.

Rows = Die 1 · Columns = Die 2 · each cell shows Y(die 1, die 2)

Measurement space

{2, 3, …, 12} — the possible values Y can take. Click one to see which outcomes in O map to it.

The distribution of Y

Bars fill in as you explore each sum above.