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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 k(3x4), -1 $3751 0, elsewhere. f(~'L') = (a) Determine k that renders x) a valid density function. {b} Calculate the mean of X. (c) Calculate the variance of X. {d} For this particular measurement. it is undesirable ifthe magnitude of the error(i.e.. |x|] exceeds 0.8. What is the probability that this occurs? (e) Find the cumulative distribution function (CDF) ofX