Let X1, X2, be a sequence of i i d random variables each having the uniform distribution on the interval 0, for some real number 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 ) converges in distribution to the distribution with c d f c Use ...

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 ...

Let X1, X2, . . . be a sequence of i.i.d. random variables each having the uniform

Question:

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.

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...