Cookie Collector: Find the Expected Number of Draws to Collect All Unique Coupons

Problem The classic coupon collector problem: there are N distinct types of coupons. Each draw gives a uniformly random coupon. Compute the expected number of draws to collect at least one of each type. Also write a simulation to verify the analytical result. Example: Follow-ups Derive the expected_draws formula from first principles using the geometric distribution. What is the variance of the number of draws? How do you derive it? If some coupons are twice as likely as others, how does the exp…