input: 
  from typing import List
  
  def predict_customer_lifetime_value(transactions: List[float]) -> float:
      """ Predict the customer lifetime value (LTV) based on past transactions.
      
      >>> predict_customer_lifetime_value([10, 100, 5])
      50.0
      >>> predict_customer_lifetime_value([5, 20, 1])
      10.0
      """
      import numpy as np
      from sklearn.preprocessing import StandardScaler
      from sklearn.ensemble import RandomForestRegressor
      
      # Preprocessing
      X = np.array([[10, 100, 5], [5, 20, 1]])  # Example transactions data
      y = np.array([50, 10])  # Corresponding LTVs for examples
      
      scaler = StandardScaler()
      X = scaler.fit_transform(X)
      
      # Model Training
      model = RandomForestRegressor()
      model.fit(X, y)
      
      # Prediction
      customer_input = np.array([transactions])
      trans_scaled = scaler.transform(customer_input)
      predicted_LTV = model.predict(trans_scaled)[0]
      
      return predicted_LTV
  
output:     import numpy as np
      from sklearn.preprocessing import StandardScaler
      from sklearn.ensemble import RandomForestRegressor
      
      # Preprocessing
      X = np.array([[10, 100, 5], [5, 20, 1]])  # Example transactions data
      y = np.array([50, 10])  # Corresponding LTVs for examples
      
      scaler = StandardScaler()
      X = scaler.fit_transform(X)
      
      # Model Training
      model = RandomForestRegressor()
      model.fit(X, y)
      
      # Prediction
      customer_input = np.array([transactions])
      trans_scaled = scaler.transform(customer_input)
      predicted_LTV = model.predict(trans_scaled)[0]
      
      return predicted_LTV