The noise output of a quadratic detector in a radio receiver can be represented as X2 + y2, where X and Yare independently and normally distributed with parameters m = 0 and σ > O. If, in addition to noise, there is a signal present, the output is represented by (X + a)2 + (Y + b)2, where a and b are given constants. Find the probability density function of the output of the detector, assuming that (i) noise alone is present, (ii) both signal and noise are present.