4. A random variable X has distribution function F(x)=1. random variable Y has distribution function F(y)=1 1 1+x² (リ 1+ y .A a. What is the value of y for the limiting Generalized Pareto Distribution for each random variable? b. What is the hazard rate for each random variable? Does this suggest tails that are heavier or lighter than an exponential distribution? c. Find the limiting density ration of X to Y. Which distribution has the heavier tail by this measure?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter10: Statistics
Section10.1: Measures Of Center
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4. A random variable X has distribution function F(x)=1.
random variable Y has distribution function F(y)=1
1
1+x²
(リ
1+ y
.A
a. What is the value of y for the limiting Generalized Pareto Distribution
for each random variable?
b. What is the hazard rate for each random variable? Does this suggest
tails that are heavier or lighter than an exponential distribution?
c. Find the limiting density ration of X to Y. Which distribution has the
heavier tail by this measure?
Transcribed Image Text:4. A random variable X has distribution function F(x)=1. random variable Y has distribution function F(y)=1 1 1+x² (リ 1+ y .A a. What is the value of y for the limiting Generalized Pareto Distribution for each random variable? b. What is the hazard rate for each random variable? Does this suggest tails that are heavier or lighter than an exponential distribution? c. Find the limiting density ration of X to Y. Which distribution has the heavier tail by this measure?
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