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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 1x. 3) = (x² +3,0 < f(x, y) +₁0 < x < 1,0 < x < 2₂ 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 1x. 3) = (x² +3,0 < f(x, y) +₁0 < x < 1,0 < x < 2₂ elsewhere. 0, a. Verify if it is a valid density function b. Find P[(X, Y) E A], where A= {(x, y)| 0

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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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 (x² + ²/²,₁0 < x < 1,0 < x < 2 f(x, y) = 0, elsewhere. a. Verify if it is a valid density function b. Find P[(X, Y) E A], where A= {(x, y)| 0<x<,/2,4 <y< ½ C. Find the marginal density g(x). d. Find the marginal density h(y).
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 (x² + ²/²,₁0 < x < 1,0 < x < 2 f(x, y) = 0, elsewhere. a. Verify if it is a valid density function b. Find P[(X, Y) E A], where A= {(x, y)| 0<x<,/2,4 <y< ½ C. Find the marginal density g(x). d. Find the marginal density h(y).
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