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Gasoline is to be stocked in a bulk tank once at the beginning of each week and then sold to individual customers. Let Y, 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 supplies, Y, varies from week to week. Let Y, denote the proportion of the capacity of the bulk tank that is sold during the week. Because Y, and Y, are both proportions, both variables take on values between 0 and 1. Further, the amount sold, y, cannot exceed the amount available, y,. Suppose that the joint density function for Y, and Y, is given by (3y1 os y2 s Y, S 1, lo, f(y,, Y2) = elsewhere. A sketch of this function is given below. 3 1 y2 (a) Find F (Round your answer to four decimal places.) (b) Find Y2 the probability that the amount sold is less than one-eighth the amount purchased. (Enter your probability as a fraction.)

Gasoline is to be stocked in a bulk tank once at the beginning of each week and then sold to individual customers. Let Y, 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 supplies, Y, varies from week to week. Let Y, denote the proportion of the capacity of the bulk tank that is sold during the week. Because Y, and Y, are both proportions, both variables take on values between 0 and 1. Further, the amount sold, y, cannot exceed the amount available, y,. Suppose that the joint density function for Y, and Y, is given by (3y1 os y2 s Y, S 1, lo, f(y,, Y2) = elsewhere. A sketch of this function is given below. 3 1 y2 (a) Find F (Round your answer to four decimal places.) (b) Find Y2 the probability that the amount sold is less than one-eighth the amount purchased. (Enter your probability as a fraction.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Gasoline is to be stocked in a bulk tank once at the beginning of each week and then sold to individual customers. Let Y, 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 supplies, Y, varies from week to week. Let Y, denote the proportion of the capacity of the bulk tank that is sold during the week. Because Y, and Y, are both proportions, both variables take on values between 0 and 1. Further, the amount sold, y,, cannot exceed the amount available, y,. Suppose that the joint density function for Y, and Y, is given by Į 3y,, os y2 s y, s 1, f(Y1, Y2) = elsewhere. A sketch of this function is given below. f(Yy» Y2) 3 - 1 (a) Find (Round your answer to four decimal places.) (b) Find the probability that the amount sold is less than one-eighth the amount purchased. (Enter your probability as a fraction.)
Transcribed Image Text:Gasoline is to be stocked in a bulk tank once at the beginning of each week and then sold to individual customers. Let Y, 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 supplies, Y, varies from week to week. Let Y, denote the proportion of the capacity of the bulk tank that is sold during the week. Because Y, and Y, are both proportions, both variables take on values between 0 and 1. Further, the amount sold, y,, cannot exceed the amount available, y,. Suppose that the joint density function for Y, and Y, is given by Į 3y,, os y2 s y, s 1, f(Y1, Y2) = elsewhere. A sketch of this function is given below. f(Yy» Y2) 3 - 1 (a) Find (Round your answer to four decimal places.) (b) Find the probability that the amount sold is less than one-eighth the amount purchased. (Enter your probability as a fraction.)
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