Ononot — Let X1, X2, \dots, Xn be i.i.d. random variables following a

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Let $X_1, X_2, \dots, X_n$ be i.i.d. random variables following a power-law distribution with PDF $f(x; \theta) = \theta x^{\theta-1}$ for $x \in (0, 1)$ and $\theta > 0$ . If we define a new random variable $Y = -\sum_{i=1}^n \ln(X_i)$ , which of the following is the probability density function of $Y$ ?