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Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (°F) at which a certain reaction starts to take place. Suppose that two random variables X and Y have the joint density f(x, y) = = {x² +,0 < x < 1,0 < y < 2, elsewhere. 0, a. Verify if it is a valid density function. b. Find P[(X, Y) E A], where A = {(x, y) | 0

Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (°F) at which a certain reaction starts to take place. Suppose that two random variables X and Y have the joint density f(x, y) = = {x² +,0 < x < 1,0 < y < 2, elsewhere. 0, a. Verify if it is a valid density function. b. Find P[(X, Y) E A], where A = {(x, y) | 0

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.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 23E
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Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (°F) at which a certain reaction starts to take place. Suppose that two random variables X and Y have the joint density f(x, y) = = {x² +,0 < x < 1,0 < y < 2, elsewhere. 0, a. Verify if it is a valid density function. b. Find P[(X, Y) E A], where A = {(x, y) | 0<x< ½, ½ <y<½. c. Find the marginal density g(x).
Transcribed Image Text:Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (°F) at which a certain reaction starts to take place. Suppose that two random variables X and Y have the joint density f(x, y) = = {x² +,0 < x < 1,0 < y < 2, elsewhere. 0, a. Verify if it is a valid density function. b. Find P[(X, Y) E A], where A = {(x, y) | 0<x< ½, ½ <y<½. c. Find the marginal density g(x).
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