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−x2), for −1≤x≤1,

f(x)=0, elsewhere.

(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., |x|)
exceeds 0.8. what is the probability that this occurs?