def _compute_nfp_real(l, u, counts, sizes):
if l > u:<EOL><INDENT>raise ValueError("<STR_LIT>")<EOL><DEDENT>return np.sum((float(sizes[u])-sizes[l:u+<NUM_LIT:1>])/float(sizes[u])*counts[l:u+<NUM_LIT:1>])<EOL>
Computes the expected number of false positives caused by using
    u to approximate set sizes in the interval [l, u], using the real
    set size distribution.

    Args:
        l: the lower bound on set sizes.
        u: the upper bound on set sizes.
        counts: the complete distribution of set sizes.
        sizes: the complete domain of set sizes.

    Return (float): the expected number of false positives.