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StatisticsQ&A Library#2: Let X1, X2 and X3 an independent and identically distributed (i.i.d.) random sample taken froma distribution with probability density function (p.d.f.) f(x). Let Y1 be the 1st order statistic ofX1, X2, and X3(a) Mathematically define Yı in terms of X1, X2, and X3, i.e. what mathematical operationswould 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)Question

Asked Oct 27, 2019

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Step 1

Let X_{1, }X_{2 }and X_{3} 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 Y_{1} be the 1^{st} order statistic of X_{1, }X_{2 }and X_{3.}

Step 3

We know th...

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