stats

🟢 Stats: Coupon Collector Problem (Meta Favorite)

"Expected rolls to see all 6 sides of a fair die?"

When you've seen k sides, P(new side) = (6-k)/6. Expected rolls for that stage = 6/(6-k).

E = 6/6 + 6/5 + 6/4 + 6/3 + 6/2 + 6/1
  = 1 + 1.2 + 1.5 + 2 + 3 + 6
  = 14.7 rolls

Generalized: For n types: E = n × (1 + 1/2 + 1/3 + ... + 1/n) = n × Hₙ (harmonic number)