input: from typing import List, Optional
  
  
  def predict_customer_lifetime_value(transactions_path: str, new_customer_data_display: List[float]) -> Optional[float]:
      """ Predict the customer lifetime value (LTV) based on the customer's past transactions.
      The function reads historical transaction data from a CSV file, performs preprocessing,
      trains a RandomForestRegressor model, and predicts the LTV for a new customer based
      on the provided data.
  
      >>> predict_customer_lifetime_value('transactions.csv', [10,100,5])
      500.0
      >>> predict_customer_lifetime_value('transactions.csv', [5,50,2])
      250.0
      """
      import pandas as pd
      import numpy as np
      from sklearn.preprocessing import StandardScaler
      from sklearn.ensemble import RandomForestRegressor
  
      # Preprocessing
      df = pd.read_csv(transactions_path)
      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 = np.array([new_customer_data_display])
      trans_scaled = scaler.transform(customer_input)
      predicted_LTV = model.predict(trans_scaled)[0]
      return predicted_LTV
output:     return predicted_LTV