Question
Asked Oct 27, 2019
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#2: Let X1, X2 and X3 an independent and identically distributed (i.i.d.) random sample taken from
a distribution with probability density function (p.d.f.) f(x). Let Y1 be the 1st order statistic of
X1, X2, and X3
(a) Mathematically define Yı in terms of X1, X2, and X3, i.e. what mathematical operations
would you take between the X's to get Yı.
(b) Find the cumulative distribution function (c.d.f.) of Y1
(c) Derive the p.d.f. of Y1 from its c.d.f (you may not cite problem 4)
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#2: Let X1, X2 and X3 an independent and identically distributed (i.i.d.) random sample taken from a distribution with probability density function (p.d.f.) f(x). Let Y1 be the 1st order statistic of X1, X2, and X3 (a) Mathematically define Yı in terms of X1, X2, and X3, i.e. what mathematical operations would you take between the X's to get Yı. (b) Find the cumulative distribution function (c.d.f.) of Y1 (c) Derive the p.d.f. of Y1 from its c.d.f (you may not cite problem 4)

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Expert Answer

Step 1

Let X1, X2 and X3 an independent and identically distributed (i.i.d) random sample taken from a distribution with probability density function (p.d.f) f(x).

Step 2

(a) Let Y1 be the 1st order statistic of X1, X2 and X3.

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Ymin (X, X,X,) min (X, min (X,X,))

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Step 3

We know th...

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a+b-la-b min (a,b) 2 a+b-la-b_a+b-(b-a) if a s b, then 2 2 2a 2 -a a+b-la-b_a+b-(a-b) if b<a, then 2 2 2b 2 -b X,+X3-(X2-X;) nin (X, .X,)=X;+X;-(x,-X,) 2

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