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. 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

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
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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.
Transcribed Image Text: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.
Transcribed Image Text: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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