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Example 2.17. Gasoline is to be stocked in a bulk tank once at the beginning of each week and then sold to individual customers. Let X denote to proportion of the capacity of the bulk tank that is available after the tank is stocked at the beginning of the week. As a result of limited supplies, X varies from week to week. Let Y denote the proportion of the capacity of the tank that is sold during the week. X and Y are both proportions so they take on values between 0 and 1. Furthermore, the amount sold, Y, cannot exceed the amount available, X. The model is given by 3r f(r, y) = 0

Example 2.17. Gasoline is to be stocked in a bulk tank once at the beginning of each week and then sold to individual customers. Let X denote to proportion of the capacity of the bulk tank that is available after the tank is stocked at the beginning of the week. As a result of limited supplies, X varies from week to week. Let Y denote the proportion of the capacity of the tank that is sold during the week. X and Y are both proportions so they take on values between 0 and 1. Furthermore, the amount sold, Y, cannot exceed the amount available, X. The model is given by 3r f(r, y) = 0

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Example 2.17. Gasoline is to be stocked in a bulk tank once at the beginning of each week and then sold to individual customers. Let X denote to proportion of the capacity of the bulk tank that is available after the tank is stocked at the beginning of the week. As a result of limited supplies, X varies from week to week. Let Y denote the proportion of the capacity of the tank that is sold during the week. X and Y are both proportions so they take on values between 0 and 1. Furthermore, the amount sold, Y, cannot exceed the amount available, X. The model is given by 3x 0 < y < x < 1 f(r, y) = elsewhere Find the probability that less than of the tank will be stocked but more than of the tank will be sold.
Transcribed Image Text:Example 2.17. Gasoline is to be stocked in a bulk tank once at the beginning of each week and then sold to individual customers. Let X denote to proportion of the capacity of the bulk tank that is available after the tank is stocked at the beginning of the week. As a result of limited supplies, X varies from week to week. Let Y denote the proportion of the capacity of the tank that is sold during the week. X and Y are both proportions so they take on values between 0 and 1. Furthermore, the amount sold, Y, cannot exceed the amount available, X. The model is given by 3x 0 < y < x < 1 f(r, y) = elsewhere Find the probability that less than of the tank will be stocked but more than of the tank will be sold.
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