Paper 2, Section I, F

Probability | Part IA, 2015

Let UU be a uniform random variable on (0,1)(0,1), and let λ>0\lambda>0.

(a) Find the distribution of the random variable (logU)/λ-(\log U) / \lambda.

(b) Define a new random variable XX as follows: suppose a fair coin is tossed, and if it lands heads we set X=U2X=U^{2} whereas if it lands tails we set X=1U2X=1-U^{2}. Find the probability density function of XX.

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