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 modelling these errors. Suppose the measurement error X of a certain physical quantity is decided by the density function f(x) = {k(3 – x²) -1

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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
modelling these errors. Suppose the measurement error X of a certain physical quantity is
decided by the density function
f(x) = {k(3 – x²) -1<x<1
elsewhere
i) Determine k that renders fAx) a valid density function.
ii) Find the probability that a random error in measurement is more than 0.3.
Transcribed Image Text: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 modelling these errors. Suppose the measurement error X of a certain physical quantity is decided by the density function f(x) = {k(3 – x²) -1<x<1 elsewhere i) Determine k that renders fAx) a valid density function. ii) Find the probability that a random error in measurement is more than 0.3.
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