Solution Found!
Refer to Exercise 4.a. Find the conditional probability
Chapter 2, Problem 6E(choose chapter or problem)
Refer to Exercise 4.
a. Find the conditional probability mass function \(p_{Y \mid X}(y \mid 1)\).
b. Find the conditional probability mass function \(p_{X \mid Y}(x \mid 2)\).
c. Find the conditional expectation \(E(Y\mid X=1)\).
d. Find the conditional expectation \(E(X\mid Y=2)\).
Equation Transcription:
Text Transcription:
p_{Y|X}(y|1)
p_{X|Y}(x|2)
E(Y|X=1)
E(X|Y=2)
Questions & Answers
QUESTION:
Refer to Exercise 4.
a. Find the conditional probability mass function \(p_{Y \mid X}(y \mid 1)\).
b. Find the conditional probability mass function \(p_{X \mid Y}(x \mid 2)\).
c. Find the conditional expectation \(E(Y\mid X=1)\).
d. Find the conditional expectation \(E(X\mid Y=2)\).
Equation Transcription:
Text Transcription:
p_{Y|X}(y|1)
p_{X|Y}(x|2)
E(Y|X=1)
E(X|Y=2)
ANSWER:
Step 1 of 5:
Here,it is given that X be the number with too little clearance and Y be the number with too much clearance.
Also the joint probability mass function of X and Y is given as
Y | ||||
X |
0 |
1 |
2 |
3 |
0 |
0.15 |
0.12 |
0.11 |
0.10 |
1 |
0.09 |
0.07 |
0.05 |
0.04 |
2 |
0.06 |
0.05 |
0.04 |
0.02 |
3 |
0.04 |
0.03 |
0.02 |
0.01 |
Using these,we have to find the required probabilities and expectations.