4. Assume the joint PMF given in Problem 1. (a) Find the correlation of X and Y. (b) Find E[X]. (d) Find the covariance of X and Y. (c) Find E[Y].
4. Assume the joint PMF given in Problem 1. (a) Find the correlation of X and Y. (b) Find E[X]. (d) Find the covariance of X and Y. (c) Find E[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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solve only problem number 4
![1. Consider the joint PMF Pxx(x,y) given in the following.
Pxy(x.y) x 0 x= 1 x=2
0.09
0.06 0.15
%3!
(a) Find P[X=1].
(c) Find P[X>Y.
(b) Find P[Y=2].
(d) Find P[Y=X+1_
y = 1
0.22
0.29
ソ=2
0.19
2. Assume the joint PMF Pxx(x,y) given in Problem 1.
(a) Find Px(x).
(c) Find P[X>Y.
(b) Find Pr(y).
(d) Find E[X].
3. Consider the joint PDF fr x(x.y) given in the following.
f x.y(r;y)= {?
(1² + y²)
if 0 <r<1. 0<y<1
otherwise.
(a) Find the marginal probability density function f(x).
(b) Calculate E[X].
(d) Calculate Var[X].
(c) Calculate E[X*].
4. Assume the joint PMF given in Problem 1.
(a) Find the correlation of X and Y.
(b) Find E[X].
(d) Find the covariance of X and Y.
(c) Find E[Y].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed180457-2ca6-4012-a54e-e269d4f35cc4%2Ff25e5be3-6b60-4fa9-a455-24cb8e0eaaab%2F21lnh54_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Consider the joint PMF Pxx(x,y) given in the following.
Pxy(x.y) x 0 x= 1 x=2
0.09
0.06 0.15
%3!
(a) Find P[X=1].
(c) Find P[X>Y.
(b) Find P[Y=2].
(d) Find P[Y=X+1_
y = 1
0.22
0.29
ソ=2
0.19
2. Assume the joint PMF Pxx(x,y) given in Problem 1.
(a) Find Px(x).
(c) Find P[X>Y.
(b) Find Pr(y).
(d) Find E[X].
3. Consider the joint PDF fr x(x.y) given in the following.
f x.y(r;y)= {?
(1² + y²)
if 0 <r<1. 0<y<1
otherwise.
(a) Find the marginal probability density function f(x).
(b) Calculate E[X].
(d) Calculate Var[X].
(c) Calculate E[X*].
4. Assume the joint PMF given in Problem 1.
(a) Find the correlation of X and Y.
(b) Find E[X].
(d) Find the covariance of X and Y.
(c) Find E[Y].
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