Z equals P X given Z times P Y given Z so it's like independence the joint between x and y is the product of marginal for X marginal for y exit that it's only true when you condition on Z once you know z x and y are independent but as long as you don't know z they might have a relationship for example z might be something I don't know like Z could be the weather and X might be is somebody carrying an umbrella and Y might be is the is the pavement wet or something and once you know it's raining you you don't need to you already know