The joint density of X and Y is given by, 6 fxr (x, y) = (x² + 0l) b) Find the marginal probability distributions of X and Y. c) Find the conditional probability density function of Y given X=0.5 and calculate P(Y

The joint density of X and Y is given by, 6 fxr (x, y) = (x² + 0l) b) Find the marginal probability distributions of X and Y. c) Find the conditional probability density function of Y given X=0.5 and calculate P(Y

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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Question

The joint density of X and Y is given by,
ху
fxy (x, y) = ;
(x²
0 <x < 1, 0 < y < 2
2
a) Calculate P(X<1, Y>1)
b) Find the marginal probability distributions of X and Y.
c) Find the conditional probability density function of Y given X-0.5 and calculate
P(Y<1\X=0.5).
d) Calculate the correlation coefficient. State whether X and Y are independent or not.

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