Let X and Y be two continuous random variables with joint probability density function:6e-(2x+3y)+kx21, y > 0fxy (x, y) =otherwisea) Find the coefficient k.b) Find P(X < 3,Y > 2).c) Find the marginal probability density functions of X and Y ( fx(x), f;(y)).d) Are X and Y independent?

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Let X and Y be two continuous random variables with joint probability density function: 6e fxy (x, y) = -(2x+3y)+k x21, y 2 0 otherwise a) Find the coefficient k. b) Find P(X < 3, Y > 2). c) Find the marginal probability density functions of X and Y (fx(x), f,(y)). d) Are X and Y independent?

Let X and Y be two continuous random variables with joint probability density function: 6e fxy (x, y) = -(2x+3y)+k x21, y 2 0 otherwise a) Find the coefficient k. b) Find P(X < 3, Y > 2). c) Find the marginal probability density functions of X and Y (fx(x), f,(y)). d) Are X and Y independent?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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Question

Let X and Y be two continuous random variables with joint probability density function:
6e-(2x+3y)+k
x21, y > 0
fxy (x, y) =
otherwise
a) Find the coefficient k.
b) Find P(X < 3,Y > 2).
c) Find the marginal probability density functions of X and Y ( fx(x), f;(y)).
d) Are X and Y independent?

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