Question: Let X1, X2, . . . be a sequence of i.i.d. random variables each having the uniform distribution on the interval [0, ] for some

Let X1, X2, . . . be a sequence of i.i.d. random variables each having the uniform on the interval [0, Î¸] for some real number Î¸ > 0. For each n, define Yn to be the maximum of X1, . . . , Xn
a. Show that the c.d.f. of Yn is

b. Show that Zn = n(Yn ˆ’ Î¸) converges in distribution to the distribution with c.d.f.

c. Use Theorem 6.3.2 to find the approximate distribution of Y2n when n is large.

0 if x s0 if y > fz 0. exp(z/8)

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a Clearly Y n y if and only if X i y for i 1 n Hence b The cdf of Zn is for z 0 PrZ n z Pr... View full answer

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