Math Problem Statement

Let Y(1) be the  rst order statistic of a random sample of size n from a distri-

bution that has pdf f(y) = e􀀀(y􀀀 );   < y < 1, zero elsewhere. What is the

limiting distribution of Zn = n(Y(1) 􀀀  )?

Solution

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Math Problem Analysis

Mathematical Concepts

Order Statistics
Probability Distributions
Exponential Distribution
Limiting Distribution

Formulas

Probability density function: f(y) = e^-(y-θ)
Zn = n(Y(1) - θ)

Theorems

Limit Theorem for Extreme Order Statistics

Suitable Grade Level

Advanced Undergraduate/Graduate Level