input: def predict_customer_lifetime_value(transactions: pd.DataFrame) -> float:
      """Train a machine learning model to predict customer lifetime value (LTV) based on past transactions.
      Given a DataFrame containing a customer's past transactions, the function preprocesses the data, trains a 
      RandomForestRegressor model, and then predicts the LTV for a new set of past transactions provided as input.
  
      >>> df = pd.DataFrame([[10, 100, 5], [20, 50, 3]], columns=['A', 'B', 'LTV'])
      >>> predict_customer_lifetime_value(df)
      4.5
      """
      X = transactions.iloc[:,:-1].values
      y = transactions.iloc[:,-1].values
      scaler = StandardScaler()
      X_scaled = scaler.fit_transform(X)
      
      model = RandomForestRegressor()
      model.fit(X_scaled, y)
      
      new_transactions = np.array([[10, 100]])  # Example input data
      new_trans_scaled = scaler.transform(new_transactions)
      predicted_LTV = model.predict(new_trans_scaled)[0]
      
      return predicted_LTV
output:     from sklearn.ensemble import RandomForestRegressor
      from sklearn.preprocessing import StandardScaler
      import numpy as np
      import pandas as pd