suppose-that-a-sample-of-size-n-8-is-drawn-from-a-population-with-PDF-f-x-x-2-9-0-lt-x-lt-3-find-1-p-1-lt-x-lt-2-2-PDF-and-CDF-of-the-fourth-smallest-O-S-

Tinku Tara June 4, 2023 Probability and Statistics 0 Comments

Question Number 187073 by Humble last updated on 13/Feb/23

suppose that a sample of size n=8 is drawn from a population with PDF: {f(x)=(x^2 /9), 0 < x < 3} find (1) p(1 < x < 2) (2) PDF and CDF of the fourth smallest O.S

$${suppose}\:{that}\:{a}\:{sample}\:{of}\:{size} \\ $$$${n}=\mathrm{8}\:{is}\:{drawn}\:{from}\:{a}\:{population}\:{with}\:{PDF}:\: \\ $$$$\left\{{f}\left({x}\right)=\frac{{x}^{\mathrm{2}} }{\mathrm{9}},\:\mathrm{0}\:<\:{x}\:<\:\mathrm{3}\right\} \\ $$$${find} \\ $$$$\left(\mathrm{1}\right)\:\:\:{p}\left(\mathrm{1}\:<\:{x}\:<\:\mathrm{2}\right) \\ $$$$\left(\mathrm{2}\right)\:\:{PDF}\:{and}\:{CDF}\:{of}\:{the}\:{fourth}\:{smallest}\:{O}.{S} \\ $$

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suppose-that-a-sample-of-size-n-8-is-drawn-from-a-population-with-PDF-f-x-x-2-9-0-lt-x-lt-3-find-1-p-1-lt-x-lt-2-2-PDF-and-CDF-of-the-fourth-smallest-O-S-

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