The discussion revolves around finding the joint probability density function (pdf) of three derived variables, Y1, Y2, and Y3, based on independent Gaussian random variables X1, X2, and X3. The relationship between these variables is established through linear combinations, with Y1 being the sum and Y2 and Y3 being differences of the X variables. Participants highlight the importance of knowing whether the original variables are continuous or discrete, as well as their potential values, to accurately determine the joint pdf. It is noted that the pdf of Y1 can be derived from the convolution of the individual pdfs of X1, X2, and X3, while Y2 and Y3 require convolution of specific pairs of these pdfs. The discussion suggests consulting Papoulis' book for a more comprehensive understanding of the topic.
