




from numpy import exp, pi, sqrt

def 			_SCREAMING_SNAKE_CASE			(							lowercase	:       int	,							lowercase	:       float = 0.0	,							lowercase	:       float = 1.0     ):


      '''simple docstring'''



      return 1 / sqrt(2 * pi * sigma**2     ) * exp(-((x - mu) ** 2) / (2 * sigma**2)     )


if __name__ == "__main__":
 import doctest

 doctest.testmod()









def 			_SCREAMING_SNAKE_CASE			(							lowercase	:       float	,							lowercase	:       list[float]     ):


      '''simple docstring'''



      if discount_rate < 0:
            raise ValueError('Discount rate cannot be negative'     )
      if not cash_flows:
            raise ValueError('Cash flows list cannot be empty'     )
      lowerCamelCase_		     =    sum(
          cash_flow / ((1 + discount_rate) ** i) for i, cash_flow in enumerate(lowercase     )     )
      return round(lowercase	,							ndigits=2     )


if __name__ == "__main__":
 import doctest

 doctest.testmod()



