Help please probability and statistics questions,,,

i. (Another Arithmetic Puzzle) Let X and Y be two independent Bernoulli(.5) random variables. Define S and T by: S=X+Y and T = X -Y. (a) Find the joint and marginal pmf's for S and T. (b) Are S and T independent. 57. Data is taken on the height and shoe size of a sample of MIT students. Height is coded by 3 values: 1 (short), 2 (average), 3 (tall) and shoe size is coded by 3 values 1 (small), 2 (average), 3 (large). The joint counts are given in the following table. Shoe \\ Height | 1 2 3 234 225 84 180 453 161 39 192 157 Practice Exam 1: All Questions, Spring 2014 10 Let X be the coded shoe size and Y the height of a random person in the sample. (a) Find the joint and marginal pif of X and Y. (b) Are X and Y independent? 58. Let X and Y be two continuous random variables with joint pdf f(r,y) = cray(1 + y) for 0 x 3 and 0 Sys 3, and f(r,y) = 0 otherwise. (a) Find the value of c. (b) Find the probability P(1 5 X