public bool ShowPreviousObservations {get; set;}

//The layer must be track aware and spatial
if (streamLayer.TrackType != TrackType.Spatial)
  return;
//Must be on QueuedTask
//get the CIM Definition
var def = streamLayer.GetDefinition() as CIMFeatureLayer;
//set the number of previous observations, 
def.PreviousObservationsCount = (int)streamLayer.GetExpirationMaxCount() - 1;
//set show previous observations and track lines to true
def.ShowPreviousObservations = true;
def.ShowTracks = true;
//commit the changes
streamLayer.SetDefinition(def);