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(a) Determine k that renders f(x) a valid density function.(b) Find the probability that a random error in measurement is less than 1/2.(c) For this particular measurement, it is undesirable if the magnitude of the error (i.e., | a:|), exceeds 0.8. What is the probability that thisoccurs?

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S fc(3 -2 -1 sa < 1. elsewhere. '0.