Measurements of scientific systems are always subject to variation, some more than others. There are many structures for measurement error, and statisticians spend a great deal of time modeling these errors. Suppose the measurement error X of a certain physical quantity is decided by the density function f(x) = [k(3-²), 10, -1≤x≤ 1, elsewhere. (a) Determine k that renders f(x) a valid density function. (b) Find the probability that a random error in measurement is more than 1/4. (c) For this particular measurement, it is undesirable if the magnitude of the error (i.e., [x]) exceeds 0.8. What is the probability that this occurs