. At a particular gas station, gasoline is stocked in a bulk tank each week. Let random variable X denote the proportion of the tank's capacity that is stocked in a given week, and let y denote the proportion of the tank's apacity that is sold in the same week. The joint pdf of X and Y is given by = {³x (3x 0 f(x,y) = if0≤y

. At a particular gas station, gasoline is stocked in a bulk tank each week. Let random variable X denote the proportion of the tank's capacity that is stocked in a given week, and let y denote the proportion of the tank's apacity that is sold in the same week. The joint pdf of X and Y is given by = {³x (3x 0 f(x,y) = if0≤y

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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Question

4. At a particular gas station, gasoline is stocked in a bulk tank each week. Let random variable X denote the
proportion of the tank's capacity that is stocked in a given week, and let y denote the proportion of the tank's
capacity that is sold in the same week. The joint pdf of X and Y is given by
f(x,y) = {³x
(3x
0
if 0 ≤ y <x< 1
otherwise
Find:
a) the probability that less than half the tank is stocked and less than a third of the tank is sold in a
random week;
b) the probability that the amount of gas sold is less than half of the amount stocked in a given week.

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8. (Same as #4) At a particular gas station, gasoline is stocked in a bulk tank each week. Let random variable X
denote the proportion of the tank's capacity that is stocked in a given week, and let y denote the proportion
of the tank's capacity that is sold in the same week. The joint pdf of X and Y is given by
if0 ≤y <x<1
otherwise
f(x,y) = {³x
(3x
0
a)
Find the marginal probability distributions of X and Y.
b) Show that the two random variables are not independent. Using part of your answer to a) is a much
shorter solution. Once you've done this with probability, using common sense is VERY straightforward.

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Page 264, 4.4.12