input: Write a function to parse a given json-formatted string into a dictionary. Return the parsed dictionary. If the string cannot be parsed, return None.
  assert json_string_to_dict('{"name": "John","age": 30,"address": {"city": "New York","state": "NY"}}')=={"name": "John","age": 30,"address": {"city": "New York","state": "NY"}}
  assert json_string_to_dict('{"name": "Jane","age": 25}')=={"name": "Jane","age": 25}
  assert json_string_to_dict('invalid json string')==None
  assert json_string_to_dict('{}')=={}
  assert json_string_to_dict('')==None
output: try:
      return json.loads(json_string)
  except json.JSONDecodeError:
      return None