Suppose that two continuous random variables X and Y have joint probability density function fxy = A( ex+y + e2x+y) , 1 ≤ x ≤ 2 ,0≤ y≤3 0 elsewhere a. P ( 3/2 ≤ X ≤ 2, 1 ≤ Y ≤ 2) b. Are the random variables X and Y independent? c. find the conditional density X given Y = 0

Suppose that two continuous random variables X and Y have joint probability density function fxy = A( ex+y + e2x+y) , 1 ≤ x ≤ 2 ,0≤ y≤3 0 elsewhere a. P ( 3/2 ≤ X ≤ 2, 1 ≤ Y ≤ 2) b. Are the random variables X and Y independent? c. find the conditional density X given Y = 0

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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Question

Suppose that two continuous random variables X and Y have joint probability density function

fxy = A( e^x+y + e^2x+y) , 1 ≤ x ≤ 2 ,0≤ y≤3

0 elsewhere

a. P ( 3/2 ≤ X ≤ 2, 1 ≤ Y ≤ 2)

b. Are the random variables X and Y independent?

c. find the conditional density X given Y = 0

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

Expert Solution