Determine if the pairs of expressions below are always equivalent. Prove your answer A. 4n + 12 and 4 (n +3)

B. m + m 3m and 3m + 2

C. 4x + 8y and 4 (x + 8y)

D. 3 (2t + 2 ) and ( t + 1 ) x 6

E. p + p and p + 7​

The discrete random variables x and y take integer values with joint probability distribution given by f (x,y) = a(y−x+1) 0 ≤ x ≤ y ≤ 2 or =0 otherwise, where a is a constant. 1 tabulate the distribution and show that a = 0.1.2 find the marginal distributions of x and y. 3 calculate cov(x,y).4 state, giving a reason, whether x and y are independent. 5 calculate e(y|x = 1).