The answers in the boxes may be incorrect. Need a second opinion with working

Let k be a positive integer and let X be a continuous random variable that is uniformly distributed on [0, k]. For any number x, denote by [x] the largest integer not exceeding x. Similarly, denote frac (x) = x - [x] to be the fractional part of x. The following are two properties of [x] and frac (x): x = [x]+frac (x) [ x] 0 for every y E {0, 1, ..., {}, and py (y) = 0 for y > e + 1. Find & and py (y) for y E {0, 1, ..., &}. Your answer should be a function of k. f = K- 1 k - 1 PY ()) = 1/k 2. Let Z = frac (x) and let fz (z) be its PDF. There exists a real number c such that fz (z) > 0 for every z E (0, c), and fz (z) = 0 for every z > c. Find c, and fz (z) for z E (0, c). C= fz ( z) = 1