考试

Suppose ( X ) is a continuous random variable with p.d.f. $f(x) = 3x^2$ for $0 \leq x \leq 1$.
Let $U$ be a $\text{Unif}(0,1)$ random variable. Which of the following functions of $U$ will give you a realization of $X$?

• (a) $X = U^{1/3}$
• (b) $X = U^{1/2}$
• (c) $X = (1/3)U^{1/3}$
• (d) $X = (1/3)U^{1/2}$
• (e) $X = 3U^2$

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