20. Let W be an standard uniform random variable. Compute the probability density function of $X = -\ln(W)$.
Added by Mary E.
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Step 1
First, we need to find the cumulative distribution function (CDF) of In(W): F(x) = P(In(W) ≤ x) = P(W ≤ e^x) Since W is a standard uniform random variable, we know that its CDF is: G(w) = P(W ≤ w) = w, for 0 ≤ w ≤ 1 Substituting e^x for w, we get: F(x) = P(W ≤ Show more…
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