Answer with full steps please

Q1 (9 marks) Find the value of the constant c so that f(x, y) satisfies the conditions of being a joint pmf for two discrete random variables X and Y. f(x, y) = c(x+y), x = 1,2,3,4. y = 1, ..., x. Q2 (18 marks) Consider a number X chosen at random from the set of numbers {1,2,3,4,5}. Then choose a number at random from the subset no larger than X, that is from {1,..., X}. Denote the second number chosen to be Y. a. Find the joint pmf of X and Y. b. Find the conditional pmf of X given Y=2. c. Are X and Y independent? Why