y x 0 1 2 0 0.10 0.11 0.05 1 0.17 0.23 0.08 2 0.06 0.14 0.06
In a certain community, levels of air pollution may exceed federal standards for ozone or for particulate matter on some days. For a particular summer season, let X be the number of days on which the ozone standard is exceeded and let Y be the number of days on which the particulate matter standard is exceeded. Assume that the joint probability mass
|
y |
|||
|---|---|---|---|
|
x |
0 |
1 |
2 |
|
0 |
0.10 |
0.11 |
0.05 |
|
1 |
0.17 |
0.23 |
0.08 |
|
2 |
0.06 |
0.14 |
0.06 |
1. Find the conditional probability mass function of pY|X(y|0). (Round the final answer to four decimal places.)
The value of pY|X(0|0)
The value of pY|X(1|0)
The value of pY|X(2|0)
2.
Find the conditional probability mass function pX|Y(x|1). (Round the final answer to four decimal places.)
The value of pX|Y(0|1)
The value of pX|Y(1|1)
The value of pX|Y(2|1)
3. Find the conditional expectation E(Y|X = 0). (Round the final answer to four decimal places.)
The value of E(Y|X = 0)
4. Find the conditional expectation E(X|Y = 1). (Round the final answer to four decimal places.)
The value of E(X|Y = 1)
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