Let x be the number of statistics majors in a certain college in the class of 2030, viewed as an r. v. each statistics major chooses between two tracks: a general track in statistical principles and methods, and a track in quantitative finance. suppose that each statistics major chooses randomly which of these two tracks to follow, independently, with probability p of choosing the general track. let y be the number of statistics majors who choose the general track, and z be the number of statistics majors who choose the quantitative finance track. (b) let n be the size of the class of 2030, where n is a known constant. for this part and the next, instead of assuming that x is poisson, assume that each of the n students chooses to be a statistics major with probability r, independently. find the joint distribution of y, z, and the number of non-statistics majors, and their marginal distributions.