Suppose that a random variable X of interest is observed. This paper concerns “the least favorable noise” Yˆϵ, which maximizes the prediction error E[X−E[X|X+Y]]2 (or minimizes variance E[X|X+Y]) in class Y with independent and varY≤ϵ2. problem was first studied by Ernst, Kagan, Rogers ([4]). In present manuscript, we show noise Yˆϵ must exist its be ϵ2. The proof existence relies on convergenc...