Square of Sums / Sum of Squares

boo.py

import numba as nb
import numpy as np
from tqdm.auto import tqdm
import dask.array as da


@nb.njit([nb.float64[:](nb.float64[:, :]),])
def g(x):
    res = np.zeros(x.shape[0], dtype=np.float64)
    for i in range(res.shape[0]):
        b, c = 0, 0
        for a in x[i]:
            b += a
            c += a**2
        res[i] = b**2 / c
    
    return res


def expected_g_uniform(n, N=1000000):
    z = da.random.uniform(0, 1, (N, n), chunks=("auto", -1))
    z = da.map_blocks(g, z, drop_axis=-1)
    return z.mean().compute()


# Find G(100; U(0, 1))
G = expected_g_uniform(100)