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Finding the constant using probability density function and cumulative distribution function
Let X be a continuous random variable with probability density function (PDF) given by:
fX(x) = cx3 + x, if 0 ≤ x ≤ 1and fX(x) = 0 otherwise.
(a) Show that the value c = 2 makes fX(x) a PDF.
(b) Find the cumulative distribution function FX(x) for every real x.
(c) What is P(â…“ ≤ X ≤ . )?
The main purpose of this exercise is to check your understanding of significance level, p-values and power .
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