3.2 Discrete random variable. Let X_i (i = 1, 2) be uniformly, independently distributed over the integers 0, 1, 2, .. ., m. Define the distance between X₁ and X₂ as

D = |X₁ - X₂|

a. Determine the pmf for D.

b. Show that E[D] = (1/3)m + (1/3)[m/(m+1)].