input: from typing import List, Union
  
  def predict_customer_ltv(transactions: List[List[Union[int, float]]]) -> float:
      """Predict the customer lifetime value given past transactions of a customer.
  
      >>> predict_customer_ltv([[10, 100, 5, ...]])
      500.0
      >>> predict_customer_ltv([[5, 50, 3, ...]])
      250.0
      """
      
      import pandas as pd
      import numpy as np
      from sklearn.preprocessing import StandardScaler
      from sklearn.ensemble import RandomForestRegressor
  
      # Data Preparation
      df_data = [[10, 100, 5, ...], [5, 50, 3, ...]] # Example transactions
      df = pd.DataFrame(df_data)
      X = df.iloc[:,:-1].values
      y = df.iloc[:,-1].values
      scaler = StandardScaler()
      X = scaler.fit_transform(X)
  
      # Model Training
      model = RandomForestRegressor()
      model.fit(X, y)
  
      # Prediction
      customer_input = transactions
      trans_scaled = scaler.transform(customer_input)
      predicted_LTV = model.predict(trans_scaled)[0]
      return predicted_LTV
output:     # Data Preparation
      df_data = transactions
      df = pd.DataFrame(df_data)
      X = df.iloc[:,:-1].values
      y = df.iloc[:,-1].values
      scaler = StandardScaler()
      X = scaler.fit_transform(X)
  
      # Model Training
      model = RandomForestRegressor()
      model.fit(X, y)
  
      # Prediction
      customer_input = transactions
      trans_scaled = scaler.transform(customer_input)
      predicted_LTV = model.predict(trans_scaled)[0]
      return predicted_LTV