input: def predict_customer_lifetime_value(transactions_df: pd.DataFrame, customer_input: np.ndarray) -> float:
      """ Predict customer lifetime value (LTV) given a customer's past transactions.
      This function first preprocesses the transaction data by scaling it. Then it trains a RandomForestRegressor model 
      on the preprocessed data. Finally, it uses the trained model to predict the LTV for a new customer based on their 
      past transaction data.
      
      >>> df = pd.DataFrame({
      ...     'transaction_1': [10, 20, 30],
      ...     'transaction_2': [100, 200, 300],
      ...     'transaction_3': [5, 15, 25],
      ...     'LTV': [1000, 2000, 3000]
      ... })
      >>> customer_input = np.array([[10, 100, 5]])
      >>> predict_customer_lifetime_value(df, customer_input)
      1000.0
      """
      
      # Preprocessing
      X = transactions_df.iloc[:,:-1].values
      y = transactions_df.iloc[:,-1].values
      scaler = StandardScaler()
      X = scaler.fit_transform(X)
      
      # Model Training
      model = RandomForestRegressor()
      model.fit(X, y)
      
      # Prediction
      trans_scaled = scaler.transform(customer_input)
      predicted_LTV = model.predict(trans_scaled)[0]
      return predicted_LTV
output:     # Preprocessing
      X = transactions_df.iloc[:,:-1].values
      y = transactions_df.iloc[:,-1].values
      scaler = StandardScaler()
      X = scaler.fit_transform(X)
      
      # Model Training
      model = RandomForestRegressor()
      model.fit(X, y)
      
      # Prediction
      trans_scaled = scaler.transform(customer_input)
      predicted_LTV = model.predict(trans_scaled)[0]
      return predicted_LTV