# Sample Questions 01 In autoharp: Semi-Automatic Grading of R and Rmd Scripts

Consider the following probability density function (pdf) over the support $(0,1)$:

\begin{equation} f(x) = \begin{cases} 4x^3 & \text{if } 0 < x < 1 \ 0 & \text{otherwise} \end{cases} \end{equation}

rf <- function(n) {
U <- runif(n)
X <- U^(1/4)
X
}


Write a function called rf, that generates i.i.d observations from this pdf. It should take in exactly one argument, $n$, that determines how many random variates to return. For instance:

set.seed(33)
rf(n = 5)


Now generate 10,000 random variates from this pdf and store them in a vector named X.

Your script must generate a function named rf and a vector named X.

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autoharp documentation built on May 30, 2021, 1:07 a.m.