Please answer all parts!! Thank you!

7. (Total 16 points) Two four-sided fair dice {the sides have numbers 1, 2, 3, 4) are rolled. Let N denote the number of dice with outcome one. Let M denote the maximum of the two dice. a.) (4 points} Find the joint distribution of N and M including the marginal disuibutions. b) {3 points) Find the conditional distribution of N given M = 3 and E[N | M = 3]. c) (5 points) Find the covariance of N and M. d} {4 points] Find the correlation of N and M