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Let X~U(0,1) and that conditional on X being observed Y|X= X~U(0,x). In logarithm ln, find f(z), the probability density function of the random variable z.

Let X~U(0,1) and that conditional on X being observed Y|X= X~U(0,x). In logarithm ln, find f(z), the probability density function of the random variable z. Make sure to define the support of z. Show sufficient work.

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