[See Solution] Let X_1, X_2, ..., X_n be independent, identically distributed random variables, each having a distribution function F_X(x). Let M=min X_1,
Question: Let \(X_{1}, X_{2}, \ldots, X_{n}\) be independent, identically distributed random variables, each having a distribution function \(F_{X}(x)\). Let \(M=\min \left\{X_{1}, X_{2}, \ldots, X_{n}\right\} .\) Find the distribution function of \(M\). Now suppose \(F_{X}\) is the uniform distribution over \((0,1)\). What is the probability density function of \(M\) ?
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