In a piston assembly, the specifications for the clearance between piston rings and the cylinder wall are very tight. In a lot of assemblies, let X be the number with too little clearance and let Y be the number with too much clearance. The joint probability mass function of X and Y is given in the table below: 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
In a piston assembly, the specifications for the clearance between piston rings and the cylinder wall are very tight. In a lot of assemblies, let X be the number with too little clearance and let Y be the number with too much clearance. The joint
|
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 |
Find the conditional probability mass function pY|X(y|1). (Round the final answer to two decimal places.)
The value of pY|X(0|1) is .
The value of pY|X(1|1) is .
The value of pY|X(2|1) is .
The value of pY|X(3|1) is
Find the conditional probability mass function pX|Y(x∣2).
pX|Y(0∣2) = (Round the final answer to one decimal place.)
pX|Y(1|2) = (Round the final answer to four decimal places.)
pX|Y(2|2) = (Round the final answer to four decimal places.)
pX|Y(3|2) = (Round the final answer to four decimal places.)
Find the conditional expectation E(Y|X = 1). (Round the final answer to two decimal places.)
Find the conditional expectation E(X|Y = 2). (Round the final answer to four decimal places.)
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