MediumProbabilitypr-165

Dirichlet Process Expected Tables

Problem

Expected number of distinct tables after n customers arrive in a Dirichlet process with concentration theta:

E[tables] = sum from i = 0 to n - 1 of theta / (theta + i).

Return 0.0 for n <= 0 or theta <= 0.

Hint

The i-th customer starts a new table with probability theta / (theta + i - 1).

case 1

in: [1,0]

expected: 0

case 2

in: [1,1]

expected: 1

case 3

in: [1,5]

expected: 2.283333333333333

case 4

in: [2,3]

expected: 2.1666666666666665

Starter codePython

def dp_expected_tables(theta, n):
    # Your code here
    pass

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