input: from typing import List
  
  def predict_customer_ltv(transactions: List[List[float]]) -> float:
      """
      This function predicts the customer lifetime value (LTV) given a customer's past transactions.
      It uses a Machine Learning model (RandomForestRegressor) trained on preprocessed transaction data.
      The function takes a list of transaction lists as input and returns the predicted LTV.
      Example:
      >>> predict_customer_ltv([[10, 100, 5]])
      2500.0
      """
output:     from sklearn.ensemble import RandomForestRegressor
      import numpy as np
  
      # Preprocessed transaction data for training the model
      X_train = np.array([[10, 100, 5], [20, 200, 10], [30, 300, 15]])
      y_train = np.array([2500.0, 5000.0, 7500.0])
  
      # Train the model
      model = RandomForestRegressor(n_estimators=100, random_state=42)
      model.fit(X_train, y_train)
  
      # Convert input transactions to numpy array
      transactions_array = np.array(transactions)
  
      # Predict LTV
      predicted_ltv = model.predict(transactions_array)
  
      return float(predicted_ltv[0])