def pmf(value):
    """
    Comvert a string into a Probability Mass Function.

    :param value:
        a sequence of probabilities summing up to 1 (no commas)
    :returns:
        a list of pairs [(probability, index), ...] with index starting from 0

    >>> pmf("0.157 0.843")
    [(0.157, 0), (0.843, 1)]
    """
    probs = probabilities(value)
    if abs(1.-sum(map(float, value.split()))) > 1e-12:
        raise ValueError('The probabilities %s do not sum up to 1!' % value)
    return [(p, i) for i, p in enumerate(probs)]
Comvert a string into a Probability Mass Function.

    :param value:
        a sequence of probabilities summing up to 1 (no commas)
    :returns:
        a list of pairs [(probability, index), ...] with index starting from 0

    >>> pmf("0.157 0.843")
    [(0.157, 0), (0.843, 1)]