(Solved): CDF, PDF, and transformations (a) Suppose \( X \) is a random variable with \ ...

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CDF, PDF, and transformations (a) Suppose \( X \) is a random variable with \( \operatorname{cdf} F(x)=\frac{e^{x}}{1+e^{x}} \). Find its density \( f \). (b) Suppose \( X \) is a random varible with pdf \( f(x)=c x(1-x) \) for \( 0