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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def get_estimators(positions_all, positions_relevant):
 """ Extracts density estimators from a judged sample of paragraph positions. Parameters positions_all : dict of (Path, float) A sample of paragraph positions from various datasets in the NTCIR-11 Math-2, and NTCIR-12 MathIR format. positions_relevant : dict of (Path, float) A sample of relevant paragraph positions from various datasets in the NTCIR-11 A subsample of relevant paragraph positions. Returns ------- (float, KernelDensity, KernelDensity) An estimate of P(relevant), and estimators of p(position), and p(position | relevant). """

    samples_all = [
        (position,) for _, positions in positions_all.items() for position in positions]
    samples_relevant = [
        (position,) for _, positions in positions_relevant.items() for position in positions]
    estimators = dict()
    estimators["P(relevant)"] = len(samples_relevant) / len(samples_all)
    LOGGER.info("Fitting prior p(position) density estimator")
    estimators["p(position)"] = KernelDensity(**KERNEL).fit(samples_all)
    LOGGER.info("Fitting conditional p(position | relevant) density estimator")
    estimators["p(position|relevant)"] = KernelDensity(**KERNEL).fit(samples_relevant)
    return (
        estimators["P(relevant)"], estimators["p(position)"], estimators["p(position|relevant)"])