Solution Found!
Bolts manufactured for a certain purpose may be classified
Chapter 2, Problem 9E(choose chapter or problem)
Bolts manufactured for a certain purpose may be classified as acceptable (suitable for the intended purpose), downgraded (unsuitable for the intended purpose but acceptable for a different purpose), or scrap (unsuitable for any purpose). In a lot of 500 bolts, let X be the number that are downgraded and let Y be the number that are scrap. Assume that the joint probability mass function of X and Y is given in the following table.
a. Find the marginal probability mass function of X.
b. Find the marginal probability mass function of Y .
c. Are X and Y independent? Explain.
d. Find \(\mu_X\) and \(\mu_Y\).
e. Find \(\sigma_X\) and \(\sigma_Y\).
f. Find \(\text {Cov}(X,Y)\).
g. Find \(\rho(X,Y)\).
Equation Transcription:
Text Transcription:
mu_X
mu_Y
sigma_X
sigma_Y
Cov(X,Y)
rho(X,Y)
Questions & Answers
QUESTION:
Bolts manufactured for a certain purpose may be classified as acceptable (suitable for the intended purpose), downgraded (unsuitable for the intended purpose but acceptable for a different purpose), or scrap (unsuitable for any purpose). In a lot of 500 bolts, let X be the number that are downgraded and let Y be the number that are scrap. Assume that the joint probability mass function of X and Y is given in the following table.
a. Find the marginal probability mass function of X.
b. Find the marginal probability mass function of Y .
c. Are X and Y independent? Explain.
d. Find \(\mu_X\) and \(\mu_Y\).
e. Find \(\sigma_X\) and \(\sigma_Y\).
f. Find \(\text {Cov}(X,Y)\).
g. Find \(\rho(X,Y)\).
Equation Transcription:
Text Transcription:
mu_X
mu_Y
sigma_X
sigma_Y
Cov(X,Y)
rho(X,Y)
ANSWER:
Answer
Step 1 of 3
Here given joint probability mass function
We need to find The marginal probability mass function of X and Y
The joint probability mass function is
X |
0 |
1 |
2 |
3 |
4 |
PX(X) |
0 |
0.06 |
0.03 |
0.01 |
0.0 |
0.0 |
0.1 |
1 |
0.06 |
0.08 |
0.04 |
0.02 |
0.0 |
0.2 |
2 |
0.04 |
0.05 |
0.12 |
0.06 |
0.03 |
0.3 |
3 |
0.0 |
0.03 |
0.07 |
0.09 |
0.06 |
0.25 |
4 |
0.0 |
0.0 |
0.02 |
0.06 |
0.07 |
0.15 |
Py(Y) |
0.16 |
0.19 |
0.26 |
0.23 |
0.16 |
1 |