(a) Each batch of chemical used in drug manufacture is tested for impurities. This percentage of impurity is X, where X is a random variable with probability density function given by. 0 < x 1, kx 1 f(x) = 4(4-x) 0 1 < x 4, otherwise, where k is a constant. i. Determine the value of k. ii. Sketch the graph of f(x). iii. Determine, for all, x, the distribution function F(x).