(a) Each batch of chemical used in drug manufacture is tested for impurities. This percentage of...

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(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). (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).