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1. The Weibull distribution has many applications in reliability engineering, survival analysis, and general insurance. Let β > 0, δ > 0. Consider the probability density function x>0 zero otherwise. Find the probability distribution of W-Xa Determine the probability distribution of W by finding the c.d.f. of W, F w(w). i Find the c.d.f. of X, Fx(x) Hint 1: u-substitution: u- Hint 2: Hint 3: Should be FX(0)-0, P(Xs) There is no such thing as a negative cumulative distribution function. Fx(o)-1. i) Find the c.d.f. of W, Fw(w) - P(Wsw) P(x*s w). iii) What is the name of the probability distribution of w? What are its parameters?

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Solutrn: tet the. pif x(0( ) รุ่@s 궈8-i e#x δ ut e u Jo dw -Buy

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