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Let X,X,, X, be a random sample of size 3 from a uniform distribution having pdf /(x:0) = θ,0 < x < 0,0 < θ, and let):く,), be the corresponding order statistics. a. Show that 2Y, is an unbi...

Let X,X,, X, be a random sample of size 3 from a uniformdistribution having pdf /(x:0) = θ,0 < x < 0,0 < θ, and let):く,), be the corresponding order statistics. a. Show that 2Y, is

Let X,X,, X, be a random sample of size 3 from a uniform
distribution having pdf /(x:0) = θ,0
0 0
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orcle) : statistic yi.<y,くy3is Solution: ex, e Here nt3.t sample size a) f ith ordder statistic is giuen o O- χで 1 220 No cus2.9 E(2%) -9 -ey2-i s an unbiased estima tor of e Pag2 LO 4 0 20 之 20 26b) Here Liketihood dup Lie 3 Let us define a function (ab) o ifarbnin ( Х, , xay2) - first-order-statistic Уз-.max (xL.xa-, Xs )一rsth.. le 3rd ordea-statistic LLO) (无) er statist ic we t-1 FC3 Θ3 2 2 8 o 1G 2 80

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Let X,X,, X, be a random sample of size 3 from a uniform distribution having pdf /(x:0) = θ,0 < x < 0,0 < θ, and let):く,), be the corresponding order statistics. a. Show that 2Y, is an unbi...
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