Revised Example 5.5

Revised Example 5.5 - y 2 , cannot exceed the amount...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1306 INTRODUCTORY STATISTICS (SEMESTER 1 2008/2009) Example 5.5 Gasoline is to be stocked in a bulk tank once at the beginning of each week and then sold to individual customers. Let Y 1 denote the proportion of the capacity of the bulk tank that is available after the tank is stocked at the beginning of the week. Because of the limited supply, Y 1 varies from week to week. Let Y 2 denote the proportion of the capacity of the bulk tank that is sold during the week. Since Y 1 and Y 2 are both proportions, it is obvious that both variables take on values between 0 and 1. Further, it is obvious that the amount sold,
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: y 2 , cannot exceed the amount available y 1 . Suppose that a model for the relative frequency for Y 1 and Y 2 is given by f ( y 1 ; y 2 ) = & 3 y 1 ; & y 2 & y 1 & 1; ; elsewhere. Find the probability that less than 1 = 2 of the tank will be stocked but more than 1 = 4 will be sold. The corresponding probability is P ± Y 1 < 1 2 and Y 2 > 1 4 ² = Z 1 = 2 Z 1 1 = 4 f ( y 1 ; y 2 ) dy 2 dy 1 = Z 1 = 2 Z y 1 1 = 4 3 y 1 dy 2 dy 1 = 3 Z 1 = 2 y 1 ³ y 2 ´ y 1 1 = 4 dy 1 = 3 Z 1 = 2 ± y 1 ± 1 4 ² y 1 dy 1 = 3 4 Z 1 = 2 y 2 1 ± y 1 4 dy 1 = 3 4 µ y 3 1 3 ± y 2 1 4 ¶ 1 = 2 = ± 3 4 ²± 1 ² 1 24 ± 1 16 = 3 32 : 1...
View Full Document

This note was uploaded on 09/06/2010 for the course STAT STAT1306 taught by Professor Prof during the Fall '08 term at HKU.

Ask a homework question - tutors are online