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A farmer is planning to fence and fertilize a rectangular plot. Let X and Y represents the width and length for the plot respectively and suppose that the fence he has in total of 20. He wants to at least have all the sides fenced, but don't need to use all the fences. He also found that this is a very irregular plot, the fertilizer needed by a certain area follows this joint density function of X and Y: f(x, y) = { 500,0< x, y elsewhere a) Find the probability that the required fence for the plot is no longer than 10 b) Find the marginal density for X c) Find the probability that the length Y is less than 1 if it is known that X is 8

A farmer is planning to fence and fertilize a rectangular plot. Let X and Y represents the width and length for the plot respectively and suppose that the fence he has in total of 20. He wants to at least have all the sides fenced, but don't need to use all the fences. He also found that this is a very irregular plot, the fertilizer needed by a certain area follows this joint density function of X and Y: f(x, y) = { 500,0< x, y elsewhere a) Find the probability that the required fence for the plot is no longer than 10 b) Find the marginal density for X c) Find the probability that the length Y is less than 1 if it is known that X is 8

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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A farmer is planning to fence and fertilize a rectangular plot. Let X and Y represents the width and length for the plot respectively and suppose that the fence he has in total of 20. He wants to at least have all the sides fenced, but don't need to use all the fences. He also found that this is a very irregular plot, the fertilizer needed by a certain area follows this joint density function of X and Y: f(x, y) = { x²y₁0 < x, y 500, 0, elsewhere a) Find the probability that the required fence for the plot is no longer than 10 b) Find the marginal density for X c) Find the probability that the length Y is less than 1 if it is known that X is 8
Transcribed Image Text:A farmer is planning to fence and fertilize a rectangular plot. Let X and Y represents the width and length for the plot respectively and suppose that the fence he has in total of 20. He wants to at least have all the sides fenced, but don't need to use all the fences. He also found that this is a very irregular plot, the fertilizer needed by a certain area follows this joint density function of X and Y: f(x, y) = { x²y₁0 < x, y 500, 0, elsewhere a) Find the probability that the required fence for the plot is no longer than 10 b) Find the marginal density for X c) Find the probability that the length Y is less than 1 if it is known that X is 8
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