Question
Determine a method to generate random observations for the following pdf:$$f(x)=\left\{\begin{array}{ll}4 x^{3} & 0<x<1 \\0 & \text { elsewhere }\end{array}\right.$$Write an $\mathrm{R}$ function that returns a random sample of observations from this pdf.
Step 1
The CDF, F(x), is the integral of the pdf from the lower limit to x. For the given pdf, the CDF is: $$ F(x)=\int_{0}^{x} 4t^{3} dt = t^{4}|_{0}^{x} = x^{4} $$ for 0 < x < 1. Show more…
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