e joint density of X and Y is given by, fxr (x, y) = (x² + 0 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

e joint density of X and Y is given by, fxr (x, y) = (x² + 0 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

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,
Iw(x, y) = (x² +:
0 <x<1,0 < y < 2
2
a) Calculate P(X<1, Y>l)
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<l\X=0.5).
d) Calculate the correlation coefficient. State whether X and Y are independent or not.

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