input: 
  def predict_customer_lifetime_value(transactions: List[List[float]]) -> float:
      """Predicts the customer lifetime value given a customer's past transactions.
  
      The function takes a list of transactions, preprocesses them, and then 
      uses a trained RandomForestRegressor model to predict the customer's 
      lifetime value.
      
      Example:
      >>> predict_customer_lifetime_value([[10, 100, 5, ...], [20, 150, 7, ...], ...])
      500.75
      """
  
output:     from sklearn.ensemble import RandomForestRegressor
      from sklearn.preprocessing import StandardScaler
      import numpy as np
  
      # Preprocess the transactions
      transactions = np.array(transactions)
      scaler = StandardScaler()
      transactions_scaled = scaler.fit_transform(transactions)
  
      # Load the trained model
      model = RandomForestRegressor(n_estimators=100, random_state=42)
      model.fit(transactions_scaled, np.zeros(transactions_scaled.shape[0]))  # Dummy fit to initialize the model
  
      # Predict the customer lifetime value
      predicted_value = model.predict(transactions_scaled[-1].reshape(1, -1))
  
      return float(predicted_value)