It is very sloppy when you come from say, analysis, where things are precisely defined, especially in more applied statistics. In my experience, any more appli

It is very sloppy when you come from say, analysis, where things are precisely defined, especially in more applied statistics. In my experience, any more applied than probability theory itself and you get omissions of very important details such as the probability space under consideration and the RVs involved in expectations, in addition to frequent inconsistencies and outright abuses of notation. These tendencies make it a harder subject for someone who is used to precise exposition to pick up.