Gasoline is to be stocked in a bulk tank once at the beginning of each week and then sold to individual customers. The joint density of Y,, the proportion of the capacity of the tank that is stocked at the beginning of the week, and Y,, the proportion of the capacity sold during the week, is given by S3y,, 0s y2 s Y1 < 1, lo, f(y,, Y2) = elsewhere. (a) Find the marginal density function for Y,. , where (b) For what values of y, is the conditional density f(y, ly,) defined? (c) What is the probability that more than half a tank is sold given that six-sevenths of a tank is stocked? (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. The joint density of Y,, the proportion of the capacity of the tank that is stocked at the beginning of the week, and Y,, the proportion of the capacity sold during the week, is given by S3y,, 0s y2 s Y1 < 1, lo, f(y,, Y2) = elsewhere. (a) Find the marginal density function for Y,. , where (b) For what values of y, is the conditional density f(y, ly,) defined? (c) What is the probability that more than half a tank is sold given that six-sevenths of a tank is stocked? (Enter your probability as a fraction.)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.6: Proportion And Variation
Problem 17E: Find the constant of proportionality. y is directly proportional to x. If x=30, then y=15.
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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.
The joint density of Y,, the proportion of the capacity of the tank that is stocked at the beginning of the week, and Y,, the proportion of the capacity sold during the week, is given by
S3y,, 0s y2 s Y1 < 1,
lo,
f(y,, Y2) =
elsewhere.
(a) Find the marginal density function for Y,.
, where
(b) For what values of y, is the conditional density f(y, ly,) defined?
(c) What is the probability that more than half a tank is sold given that six-sevenths of a tank is stocked? (Enter your probability as a fraction.)
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