Question 5. (Graded, 20 points) Extension of hypergmmetric distribution: inside a box there areatotal ofN belleamong which, M1 arered, M2 areblue and...

Extension of hypergeometric distribution: inside a box there are a total of N balls - among which, M1 are red, M2 are blue and the rest N −M1 −M2 balls are green. Now randomly select n (0 < n ≤ N) balls from the box without replacement. Each ball has equal chance to be selected. Let X and Y denote the number of red and blue balls, respectively.a) Determine the joint distribution of X, Y , that is, calculate P(X=x,Y =y)and you need to determine the range of the pair of variables (x, y). b) Calculate E[X], E[Y ] and E[XY ].