10 - April 2008 THE UNIVERSITY OF HONG KONG DEPARTMENT OF...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: April 2008 THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1302 PROBABILITY AND STATISTICS II Example Class 10 1. Let X 1 be a random variable having the pdf f ( x | λ ) = λ- 1 exp {- x/λ } , x > 0. Let x 1 be a realization of X 1 . (a) Show that P ( X 1 /λ ≤ u ) = 1- e- u ,u > . (b) Using (a), show how to find λ α ( X 1 ) such that P { λ α ( X 1 ) ≤ λ } = 1- α, for all λ > . How would u call the statistic λ α ( x 1 )? 2. At a busy telephone exchange, the times between the arrivals of the first 10 calls to arrive after 3:15pm one day are (in second) 4.10, 5.64, 1.16, 3.45, 0.91, 0.34, 0.44, 1.28, 0.64, 1.15, and the interarrival times of the first 10 calls to arrive after 6:15pm that same day are 0.37,0.69, 1.46, 0.19, 3.75, 0.64, 1.33, 1.65, 3.11, 0.95. Assume the data sets observed after 3:15pm and after 6:15pm constitute two independent exponential random samples with mean interarrival times θ 1 and θ 2 respectively....
View Full Document

Page1 / 3

10 - April 2008 THE UNIVERSITY OF HONG KONG DEPARTMENT OF...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online