The error, X, in measuring the length of a rivet (in micrometers) has the following probability density function f(x)= 20·x·(3−x)3 243   for  0 ≤ x ≤ 3  and 0 otherwise. a) What is the probability that X > 1?  b) What is the probability that X < 1?  c) What is the probability that 2.1 < X < 2.7?  d) What is the expected value of X (E(X))?

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