Uniform distribution transformations

Given X has a uniform distribution, find the CDF or PDF of a transformed variable Y = g(X) such as Y = X², Y = sin(X), or Y = e^X.

1 questions · Challenging +1.2

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OCR S3 2016 June Q8
10 marks Challenging +1.2
8 The radius, \(R\), of a sphere is a random variable with a continuous uniform distribution between 0 and 10 .
  1. Find the cumulative distribution function and probability density function of \(A\), the surface area of the sphere.
  2. Find \(\mathrm { P } ( \mathrm { A } \leqslant 200 \pi )\). \section*{END OF QUESTION PAPER}