n 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 function of X and Y is given in the following table:
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 |
Find the conditional probability mass function of pY|X(y|0). Round the answers to four decimal places.
The value of pY|X(0|0) is .
The value of pY|X(1|0) is .
The value of pY|X(2|0) is .
P(X = 0) = 0.1 + 0.11 + 0.05 = 0.26
P(Y = 0 = | X = 0) = P(Y = 0 and X = 0) / P(X = 0) = 0.1 / 0.26 = 0.3846
P(Y = 1 = | X = 0) = P(Y = 1 and X = 0) / P(X = 0) = 0.11 / 0.26 = 0.4231
P(Y = 2 = | X = 0) = P(Y = 2 and X = 0) / P(X = 0) = 0.05 / 0.26 = 0.1923
n a certain community, levels of air pollution may exceed federal standards for ozone or for...
ques 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 function of X and Y is given in the following table: Find the marginal probability mass function...
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