Solution Found!
Refer to Exercise 9.a. Find the conditional probability
Chapter 2, Problem 11E(choose chapter or problem)
Refer to Exercise 9.
a. Find the conditional probability mass function \(p_{Y \mid X}(y \mid 4)\).
b. Find the conditional probability mass function \(p_{X \mid Y}(x \mid 3)\).
c. Find the conditional expectation \(E(Y \mid X=4)\).
d. Find the conditional expectation \(E(X \mid Y=3)\).
Equation Transcription:
Text Transcription:
p_{Y|X}(y|4)
p_{X|Y}(x|3)
E(Y|X=4)
E(X|Y=3)
Questions & Answers
QUESTION:
Refer to Exercise 9.
a. Find the conditional probability mass function \(p_{Y \mid X}(y \mid 4)\).
b. Find the conditional probability mass function \(p_{X \mid Y}(x \mid 3)\).
c. Find the conditional expectation \(E(Y \mid X=4)\).
d. Find the conditional expectation \(E(X \mid Y=3)\).
Equation Transcription:
Text Transcription:
p_{Y|X}(y|4)
p_{X|Y}(x|3)
E(Y|X=4)
E(X|Y=3)
ANSWER:
Solution:
Step 1 of 4:
Bolt manufactured for a certain for a certain purpose classified as acceptable,downgraded or scrap. In a lot of 500 bolts, if X denote the number of downgraded bolts, Y dente the number of scraps. The joint probability mass function of X and Y is given . here we can find the marginal probability function by adding the rows and columns.
Y |
||||||
X |
0 |
1 |
2 |
3 |
4 |
|
0 |
0.06 |
0.03 |
0.01 |
0 |
0 |
0.1 |
1 |
0.06 |
0.08 |
0.04 |
0.02 |
0 |
0.2 |
2 |
0.04 |
0.05 |
0.12 |
0.06 |
0.03 |
0.3 |
3 |
0 |
0.03 |
0.07 |
0.09 |
0.06 |
0.25 |
4 |
0 |
0 |
0.02 |
0.06 |
0.07 |
0.15 |
0.16 |
0.19 |
0.26 |
0.23 |
0.16 |
.
We have to find
- The conditional probability mass function PY/X(y/4).
- The conditional probability mass function PX/Y(x/3).
- The conditional expectation E (Y/X=4).
- The conditional expectation E (X/Y=3).