Continuous random variables X and Y have joint density function f(x, y) = K(x² + xy), 0< x < 1, 0 < y< 1, where K is a constant. a) Find K and the joint density function. f(x, y) 0 < x < 1, 0< y< 1 b) Find the probability that X is less than 0.8 and Y is less than 0.6. P(X < 0.8, Y < 0.6) c) Find the marginal density function for X. fx(x) = 0 < x <1 d) Find the marginal density function for Y. fr(y) : 0 < y<1

Continuous random variables X and Y have joint density function f(x, y) = K(x² + xy), 0< x < 1, 0 < y< 1, where K is a constant. a) Find K and the joint density function. f(x, y) 0 < x < 1, 0< y< 1 b) Find the probability that X is less than 0.8 and Y is less than 0.6. P(X < 0.8, Y < 0.6) c) Find the marginal density function for X. fx(x) = 0 < x <1 d) Find the marginal density function for Y. fr(y) : 0 < y<1

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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Continuous random variables X and Y have joint density function f(x, y) = K(x² + xy), 0< x < 1,
0 < y< 1, where K is a constant.
a) Find K and the joint density function.
f(x, y)
0 < x < 1, 0< y< 1
b) Find the probability that X is less than 0.8 and Y is less than 0.6.
P(X < 0.8, Y < 0.6)
c) Find the marginal density function for X.
fx(x) =
0 < x <1
d) Find the marginal density function for Y.
fr(y) :
0 < y<1

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