Expected Distinct Coupons

Problem

Expected number of distinct coupons collected after draws independent uniform draws from n coupon types.

E[distinct] = n * (1 - (1 - 1/n)^draws), using linearity of expectation over indicators. Return 0.0 for n <= 0 or draws < 0.

Hint

Each coupon type is missing with probability (1 - 1/n)^draws.

case 1

in: [365,365]

expected: 230.90815395794158

case 2

in: [6,1]

expected: 0.9999999999999998

case 3

in: [6,0]

expected: 0

case 4

in: [10,100]

expected: 9.999734386011124

Starter codePython

def expected_distinct_coupons(n, draws):
    # Your code here
    pass

4 test cases · run your code against them in the editor