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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 maximum_likelihood_estimator(self, data, states):
 """ Fit using MLE method. Parameters data: pandas.DataFrame or 2D array Dataframe of values containing samples from the conditional distribution, (Y|X) and corresponding X values. states: All the input states that are jointly gaussian. Returns ------- beta, variance (tuple):
 Returns estimated betas and the variance. """

        x_df = pd.DataFrame(data, columns=states)
        x_len = len(self.evidence)

        sym_coefs = []
        for i in range(0, x_len):
            sym_coefs.append('b' + str(i + 1) + '_coef')

        sum_x = x_df.sum()
        x = [sum_x['(Y|X)']]
        coef_matrix = pd.DataFrame(columns=sym_coefs)

        # First we compute just the coefficients of beta_1 to beta_N.
        # Later we compute beta_0 and append it.
        for i in range(0, x_len):
            x.append(self.sum_of_product(x_df['(Y|X)'], x_df[self.evidence[i]]))
            for j in range(0, x_len):
                coef_matrix.loc[i, sym_coefs[j]] = self.sum_of_product(
                    x_df[self.evidence[i]], x_df[self.evidence[j]])

        coef_matrix.insert(0, 'b0_coef', sum_x[self.evidence].values)
        row_1 = np.append([len(x_df)], sum_x[self.evidence].values)
        coef_matrix.loc[-1] = row_1
        coef_matrix.index = coef_matrix.index + 1  # shifting index
        coef_matrix.sort_index(inplace=True)

        beta_coef_matrix = np.matrix(coef_matrix.values, dtype='float')
        coef_inv = np.linalg.inv(beta_coef_matrix)
        beta_est = np.array(np.matmul(coef_inv, np.transpose(x)))
        self.beta = beta_est[0]

        sigma_est = 0
        x_len_df = len(x_df)
        for i in range(0, x_len):
            for j in range(0, x_len):
                sigma_est += self.beta[i + 1] * self.beta[j + 1] * (self.sum_of_product(
                    x_df[self.evidence[i]], x_df[self.evidence[j]]) / x_len_df - np.mean(x_df[self.evidence[i]]) * np.mean(x_df[self.evidence[j]]))

        sigma_est = np.sqrt(
            self.sum_of_product(
                x_df['(Y|X)'],
                x_df['(Y|X)']) /
            x_len_df -
            np.mean(
                x_df['(Y|X)']) *
            np.mean(
                x_df['(Y|X)']) -
            sigma_est)
        self.sigma_yx = sigma_est
        return self.beta, self.sigma_yx