Find the distribution of X(m) and Show that 2nY n where Y = Show that 2 In () Xân- Xi,

MATLAB: An Introduction with Applications
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Chapter1: Starting With Matlab
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12. Let (*1, 12, ., r„) be independent samples from the uniform distribution on [0,0]. Let
X(n) and X(1) be the maximum and minimum order statistics respectively,
(a) Find the distribution of X(m) and X(a) and hence, their means and variances.
X{n)
(b) Show that 2nY x where Y = – In
%3D
(c) Show that 2)
In
- Xản: Hence write a function of the geometric mean,
i=1
(II
GM(r) =
which is Xn
1
Transcribed Image Text:12. Let (*1, 12, ., r„) be independent samples from the uniform distribution on [0,0]. Let X(n) and X(1) be the maximum and minimum order statistics respectively, (a) Find the distribution of X(m) and X(a) and hence, their means and variances. X{n) (b) Show that 2nY x where Y = – In %3D (c) Show that 2) In - Xản: Hence write a function of the geometric mean, i=1 (II GM(r) = which is Xn 1
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