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1.1 Let Y₁ ≤Y₂ ≤Y, denote the order statistics of a random sample of size 3 from a distribution with probability density function (p.d.f.) f(x) = 1, 0

1.1 Let Y₁ ≤Y₂ ≤Y, denote the order statistics of a random sample of size 3 from a distribution with probability density function (p.d.f.) f(x) = 1, 0

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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1.1 Let Y, ≤Y₂ ≤Y, denote the order statistics of a random sample of size 3 from a distribution with probability density function (p.d.f.) f(x) = 1, 0<x< 1, zero elsewhere. Let Z= (Y₁+ Y3)/2 be the midrange of the sample. Find the p.d.f. of Z. C 1.2 Determine the probability density function, mean, variance, median and quartiles of the extreme value distribution with, P(X ≤x) = 1- exp{-e(x-μ)/"} What kind of distribution is this? 10 1.3 If V has the standard Gumble distribution and X = a + bV, determine E(a + bV) and var (a+bV). 1.4 If X has the standard exponential distribution, then U = In X has the standard extreme value distributions for minimums. 1.5 If U has the standard extreme value distribution for minimums then X=eº has the standard exponential distribution.
Transcribed Image Text:1.1 Let Y, ≤Y₂ ≤Y, denote the order statistics of a random sample of size 3 from a distribution with probability density function (p.d.f.) f(x) = 1, 0<x< 1, zero elsewhere. Let Z= (Y₁+ Y3)/2 be the midrange of the sample. Find the p.d.f. of Z. C 1.2 Determine the probability density function, mean, variance, median and quartiles of the extreme value distribution with, P(X ≤x) = 1- exp{-e(x-μ)/"} What kind of distribution is this? 10 1.3 If V has the standard Gumble distribution and X = a + bV, determine E(a + bV) and var (a+bV). 1.4 If X has the standard exponential distribution, then U = In X has the standard extreme value distributions for minimums. 1.5 If U has the standard extreme value distribution for minimums then X=eº has the standard exponential distribution.
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