The clearance in mm of a certain drill hole, has the following cumulative distribution function F: F(x) = 0 for x < 0 and F(x)= 1.25.x - 0.25.x5 for 0 ≤ x ≤ 1 and F(x) = 1 for x > 1 a) What is the probability density function for X for 0 ≤ x ≤ 1? f(x) = 2.x f(x) = 0.625.x²6 6 f(x) = 1.25-x² -0.25-x6 6 Of(x) = 1.25.x² 2 f(x) = 1.25 1.25.x4 b) What is the probability that X > 0.5? .383 c) What is the probability X < 0.5 ? .617 d) What is the probability that X < 0? 0 e) What is the probability that X > 0.7 ? .833 f) What is the probability that X > 0.7 given that X > 0.5 ? g) Calculate the median of X. h) Calculate the expected value of X? i) Calculate the expected value of x²? j) Calculate the variance of X? k) What is the probability that X is more than 0.1 below its expected value?