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0 Find the marginal probability distributions of X and Y. otherwise a) 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.

0 Find the marginal probability distributions of X and Y. otherwise a) 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.

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.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
Section2.CR: Chapter 2 Review
Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...
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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 f(x,y) (3x if 0 ≤ y < x < 1 = 0 otherwise 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 f(x,y) (3x if 0 ≤ y < x < 1 = 0 otherwise 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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