(a) Verify that fx,y is indeed a probability density function. (b) Find the marginal probability density function fx and state the name of the distribution of X. (c) Find the conditional probability density function fy|x=r.
(a) Verify that fx,y is indeed a probability density function. (b) Find the marginal probability density function fx and state the name of the distribution of X. (c) Find the conditional probability density function fy|x=r.
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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Transcribed Image Text:Question 1
function given by
Suppose that X and Y have a joint probability density
[7e-2-Ty
fx,y (x, y) =
=
(a) Verify that fx,y is indeed a probability density function.
(b) Find the marginal probability density function fx and state the name of the
distribution of X.
if x, y ≥ 0
otherwise
(c) Find the conditional probability density function fy|x=r.
(d) Are the random variables X and Y independent? Justify your answer.
(e) Let another probabilty density fx,y be given by
-(√I+√Y)²+2√IY
fx,y (x, y) =
=
ce
0
if x ≥ y ≥0
otherwise
Determine the normalization constant c in this case. Are X and Y statistically
independent? Justify your answer.
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