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3.4 Let X,, X be a random sample of size n from the U(Q,62) distribution, 6, and let Y, and Yn be the smallest and the largest order statistics of the Xs (i) Use formulas (28) and (29) in Chapter 6 to obtain the p.d.f.s of Y and Y and then, by calculating depending only on Yi and 1,- Part i. (Note: it is not saying to find the joint pdf of Yi and Yn Find their marginal Theorem 13 the EAs and Ee Y construct unbiased estimates of the mean (a + a ) / 2 and of the range θ pdfs. The Calculus is a bit ugly, would not be a bad idea to try these yourselves, but Let Xi,...,X be i.i.d. r.v.s with d.f. F and p.d.f.fwhich is positive and continuous for (-oos) ax<b (soo) and zero otherwise, and let Yı,..., Yx be the order statistics. Then the p.d.f.s giand g ofYand Y respectively, are given by (28) 0 otherwise, and (29) otherwise

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