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  3. 1 the weibull distribution has many applications in reliability engineering...

Question: 1 the weibull distribution has many applications in reliability engineering...

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1. The Weibull distribution has many applications in reliability engineering, survival analysis, and general insurance. function Let p> 0, δ > 0. Consider the probability density x>0 zero otherwise. Find the probability distribution of w-x6 a) Determine the probability distribution of W by finding the c.d.f. of W, Fw(w). Find the cd.f. of X, Fx(x) = P(X x). “Hint, 1: u-substitution: u Hint 2: There is no such thing as a negative cumulative distribution function Hint 3: Should be Fx(0)-0, Fx(o)1 i) Find the c.d.f. of W, Fw(w) - P(Wsw) P(x8s w). iii) What is the name of the probability distribution of W? What are its parameters? b) Determine the probability distribution of W by finding the p.d.f. of W, Jw(w), using the change-of-variable technique. DFind the pdf. of W. w(w) -Ax(e (w)) a ii) What is the name of the probability distribution of W? What are its parameters? dx

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. What is the name of the probability distribution of W? What are its parameters?

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