text: from __future__ import annotations
  import numpy as np
  from numpy.linalg import inv, det, slogdet
  
  
  class UnivariateGaussian:
      """
      Class for univariate Gaussian Distribution Estimator
      """
      def __init__(self, biased_var: bool = False) -> UnivariateGaussian:
          """
          Estimator for univariate Gaussian mean and variance parametersx
  
          Parameters
          ----------
          biased_var : bool, default=False
              Should fitted estimator of variance be a biased or unbiased estimator
  
          Attributes
          ----------
          fitted_ : bool
              Initialized as false indicating current estimator instance has not been fitted.
              To be set as True in `UnivariateGaussian.fit` function.
  
          mu_: float
              Estimated expectation initialized as None. To be set in `UnivariateGaussian.fit`
              function.
  
          var_: float
              Estimated variance initialized as None. To be set in `UnivariateGaussian.fit`
              function.
          """
          self.biased_ = biased_var
          self.fitted_, self.mu_, self.var_ = False, None, None
  
      def fit(self, X: np.ndarray) -> UnivariateGaussian:
          """
          Estimate Gaussian expectation and variance from given samples
  
          Parameters
          ----------
          X: ndarray of shape (n_samples, )
              Training data
  
          Returns
          -------
          self : returns an instance of self.
  
          Notes
          -----
          Sets `self.mu_`, `self.var_` attributes according to calculated estimation (where
          estimator is either biased or unbiased). Then sets `self.fitted_` attribute to `True`
          """
          self.mu_ = np.mean(X)
          if self.biased_:
              self.var_ = np.var(X)
          else:
              self.var_ = np.var(X, ddof=1)
          self.fitted_ = True
          return self
  
      def pdf(self, X: np.ndarray) -> np.ndarray:
          """
          Calculate PDF of observations under Gaussian model with fitted estimators
  
          Parameters
          ----------
          X: ndarray of shape (n_samples, )
              Samples to calculate PDF for
  
          Returns
          -------
          pdfs: ndarray of shape (n_samples, )
              Calculated values of given samples for PDF function of N(mu_, var_)
  
          Raises
          ------
          ValueError: In case function was called prior fitting the model
          """
          if not self.fitted_:
              raise ValueError("Estimator must first be fitted before calling `pdf` function")
  
          return 1/(np.sqrt(2*np.pi*self.var_)) * np.exp((-1/(2*self.var_))*(np.power(X-self.mu_, 2)))
  
  
      @staticmethod
      def log_likelihood(mu: float, sigma: float, X: np.ndarray) -> float:
          """
          Calculate the log-likelihood of the data under a specified Gaussian model
  
          Parameters
          ----------
          mu : float
              Expectation of Gaussian
          sigma : float
              Variance of Gaussian
          X : ndarray of shape (n_samples, )
              Samples to calculate log-likelihood with
  
          Returns
          -------
          log_likelihood: float
              log-likelihood calculated
          """
          samples_count = len(X)
          return ((-0.5 * samples_count) * (np.log(2 * np.pi * sigma))) + \
                 ((-1 / (2 * sigma)) * ((X.transpose() @ X) - 2 * samples_count * mu * (np.mean(X)) +
                                        samples_count * np.power(mu, 2)))
  
  
  class MultivariateGaussian:
      """
      Class for multivariate Gaussian Distribution Estimator
      """
      def __init__(self):
          """
          Initialize an instance of multivariate Gaussian estimator
  
          Attributes
          ----------
          fitted_ : bool
              Initialized as false indicating current estimator instance has not been fitted.
              To be set as True in `MultivariateGaussian.fit` function.
  
          mu_: ndarray of shape (n_features,)
              Estimated expectation initialized as None. To be set in `MultivariateGaussian.fit`
              function.
  
          cov_: ndarray of shape (n_features, n_features)
              Estimated covariance initialized as None. To be set in `MultivariateGaussian.fit`
              function.
          """
          self.mu_, self.cov_ = None, None
          self.fitted_ = False
  
      def fit(self, X: np.ndarray) -> MultivariateGaussian:
          """
          Estimate Gaussian expectation and covariance from given samples
  
          Parameters
          ----------
          X: ndarray of shape (n_samples, n_features)
              Training data
  
          Returns
          -------
          self : returns an instance of self
  
          Notes
          -----
          Sets `self.mu_`, `self.cov_` attributes according to calculated estimation.
          Then sets `self.fitted_` attribute to `True`
          """
  
          self.mu_ = np.mean(X, axis=0)
          X_wave = X - self.mu_
          self.cov_ = (1 / (X.shape[0]-1)) * np.dot(np.transpose(X_wave), X_wave)
          self.fitted_ = True
          return self
  
      def pdf(self, X: np.ndarray):
          """
          Calculate PDF of observations under Gaussian model with fitted estimators
  
          Parameters
          ----------
          X: ndarray of shape (n_samples, n_features)
              Samples to calculate PDF for
  
          Returns
          -------
          pdfs: ndarray of shape (n_samples, )
              Calculated values of given samples for PDF function of N(mu_, cov_)
  
          Raises
          ------
          ValueError: In case function was called prior fitting the model
          """
          if not self.fitted_:
              raise ValueError("Estimator must first be fitted before calling `pdf` function")
  
          X_wave = X - self.mu_
          MD = np.dot((X_wave), np.dot(inv(self.cov_), np.transpose(X_wave)))
          return (1 / (np.sqrt(det(2 * np.pi * self.cov_))) * np.exp(-0.5 * MD))
  
  
      @staticmethod
      def log_likelihood(mu: np.ndarray, cov: np.ndarray, X: np.ndarray) -> float:
          """
          Calculate the log-likelihood of the data under a specified Gaussian model
  
          Parameters
          ----------
          mu : ndarray of shape (n_features,)
              Expectation of Gaussian
          cov : ndarray of shape (n_features, n_features)
              covariance matrix of Gaussian
          X : ndarray of shape (n_samples, n_features)
              Samples to calculate log-likelihood with
  
          Returns
          -------
          log_likelihood: float
              log-likelihood calculated over all input data and under given parameters of Gaussian
          """
          samples_count = X.shape[0]
          variate_count = X.shape[1]
          const = (-0.5 * samples_count) * (variate_count * np.log(2 * np.pi) + np.log(det(cov)))
          for sample in X:
              const += -0.5 * ((sample-mu) @ inv(cov) @ (sample-mu).transpose())
          return const
  
  