input: from typing import List
  
  def predict_customer_lifetime_value(transactions_csv: str, customer_input: List[List[float]]) -> float:
      """ Predicts the customer lifetime value based on past transactions and a new customer input.
      The function loads transaction data from a CSV file, preprocesses it, trains a RandomForestRegressor,
      and then predicts the lifetime value for a given input.
      >>> predict_customer_lifetime_value('transactions.csv', [[10,100,5]])
      2500
      """
output:     import pandas as pd
      from sklearn.ensemble import RandomForestRegressor
      from sklearn.model_selection import train_test_split
      from sklearn.preprocessing import StandardScaler
  
      # Load the transaction data from CSV
      df = pd.read_csv(transactions_csv)
  
      # Preprocess the data
      X = df.drop('lifetime_value', axis=1)
      y = df['lifetime_value']
  
      # Split the data into training and testing sets
      X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)
  
      # Standardize the features
      scaler = StandardScaler()
      X_train = scaler.fit_transform(X_train)
      X_test = scaler.transform(X_test)
  
      # Train the RandomForestRegressor
      model = RandomForestRegressor(n_estimators=100, random_state=42)
      model.fit(X_train, y_train)
  
      # Preprocess the customer input
      customer_input = scaler.transform(customer_input)
  
      # Predict the customer lifetime value
      predicted_value = model.predict(customer_input)
  
      return predicted_value[0]