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1. The Weibull distribution has many applications in reliability engineering, survival analysis, and general insurance. function Let β > 0, δ > O. Consider the probability density fx(x) = βδΧ6-1 e-Px®, x>0, zero otherwise. Find the probability distribution of W-Xb) Determine the probability distribution of W by finding the p.d.f. of W, fw(w), using the change-of-variable technique D) Find the p.d.f. of W, w)-x(w ii What is the name of the probability distribution of W? What are its parameters?

c Determine the probability distribution of W by finding the m.g.f. of W, Mw(t). i)Find the m.g.f. of w, Mw(t) E(eW) E(eX). Hint 1:u-substitution: u-v». Hint, 2: Must have t < β for the integral to converge. ii What is the name of the probability distribution of W? What are its parameters?

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dn てt W od dur ト 0 /s in (으 n っ

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