Problem 1 Two statistically dependent random variables X, and X2 are applied at the inputs of a threshold detector (see Figure). The output of the detector is equal to the number of inputs that exceed the threshold T. Thus Y = 0, 1, or 2. Determine the density function py(y) in terms of the known joint density PX1,X2 (X1, X2) and T. X1 Threshold Y Detector X2