MediumProbabilitypr-122

Expected Birthday Collisions

Problem

Expected number of colliding pairs among n people whose birthdays are uniform over days days:

E[pairs] = C(n, 2) / days.

Return 0.0 for n < 2 or days <= 0.

Hint

Use indicators for each pair and linearity of expectation.

case 1

in: [23,365]

expected: 0.6931506849315069

case 2

in: [2,365]

expected: 0.0027397260273972603

case 3

in: [57,365]

expected: 4.372602739726028

case 4

in: [1,365]

expected: 0

Starter codePython

def expected_birthday_collisions(n, days):
    # Your code here
    pass

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