Let X denote the amount of space occupied by an article placed in a 1-ft³ packing container. The pdf of X is below. f(x) = {0x³(1-x) <<1 (a) Graph the pdf. otherwise f(x) 4 3 2 1 f(x) 3 2 1 x 0.2 0.4 0.6 0.8 1.0 Obtain the cdf of X. x 0.2 0.4 0.6 0.8 1.0 0 x < 0 F(x) = 0 ≤ x ≤ 1 1 x > 1 Graph the cdf of X. F(X) 1.0 0.8 0.6 0.4 0.2 F(X) 1.0 0.8 0.6 0.4 0.2 0.2 0.4 0.6 0.8 1.0 x 0.2 0.4 0.6 0.8 1.0 f(x) 4 3 2 1 f(x) 3 2 1 F(X) ཀྲྀཎྜ ཨཱུ་ ུ་ཛྱཱ་ སྦེ 1.0 F(X) 1.0 0.8 0.6 0.4 0.2 WebAssign Plot x 0.2 0.4 0.6 0.8 1.0 x 0.2 0.4 0.6 0.8 1.0 x 0.2 0.4 0.6 0.8 1.0 (b) What is P(X ≤ 0.65) [i.e., F(0.65)]? (Round your answer to four decimal places.) 0.2 0.4 0.6 0.8 1.0 (c) Using the cdf from (a), what is P(0.25 < x < 0.65)? (Round your answer to four decimal places.) What is P(0.25 ≤ X ≤ 0.65)? (Round your answer to four decimal places.) (d) What is the 75th percentile of the distribution? (Round your answer to four decimal places.) (e) Compute E(X) and x. (Round your answers to four decimal places.) E(X) = (f) What is the probability that X is more than 1 standard deviation from its mean value? (Round your answer to four decimal places.)