Description
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A village contains only kids and adults. The probability of a random citizen being a kid is given by P (kid) and that of an adult is P (adult). Each person is also having a discrete attribute called height denoted by x, which takes values in the set f4:9; 5:0; 5:1; 5:2; 5:3; 5:4; 5:5; 5:6; 5:7; 5:8g. The probability of height given that the person is a kid and adult is given by
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p(xjkid) = [0:1; 0:1; 0:1; 0:1; 0:1; 0:1; 0:1; 0:1; 0:1; 0:1] |
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and |
p(xjadult) = [0:02; 0:02; 0:02; 0:02; 0:02; 0:18; 0:18; 0:18; 0:18; 0:18] |
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(a) |
Implement an environment called village that produces a random person in this village, |
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i.e., it gives out the two tuple (kid/adult,height). Query the environment for say n = 100, |
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1000 times and then show the histograms for age, height, height given age. |
[25] |
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Implement an agent which is initialized with P (kid) = p as input. The agent should also contain another method which maps the height attribute to deciding adult or kid, using
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Bayes Rule.
[15]
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Computing the expected loss of a given decision: Initialize the agent as well as environment, query the environment some n = 100, 1000 or 10000 times. Pass the height attribute to
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the agent and get the decision. The loss is 1 if the decision is not same as the state,
otherwise it is 0. Average the loss over n, and print it.
[10]
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A village contains kids as well as adults. The probability of kids is given by P (kid) and that of adult by P (adult). Each person is also having a continuous attribute called height denoted by x
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(a) Repeat Q.1 for the following (see gure below):
[10]
(b) Repeat Q.1 when p(x kid) = p2 1 e
2
1
2
and p(x adult) =
p2 2 e
2
2
2
are
j
1
1
x 1
j
1
1
x 2
both one-dimensional Gaussian random variables.
[10]
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Repeat Q 2.2, with two attributes namely height and weight, i.e., x = (x1; x2), where x1 denotes height and x2 denotes weight.
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p(x kid) = |
1 |
e |
2 |
x |
1 1111 |
2 |
1 |
e |
2 |
x |
2 1212 |
2 |
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j |
p |
1 |
p |
1 |
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2 11 |
2 12 |
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and |
1 |
1 2121 |
2 |
1 |
2 2222 |
2 |
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p(x adult) = |
e |
2 |
x |
e |
2 |
x |
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j |
p |
1 |
p |
1 |
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2 21 |
2 22 |
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[20]
End of paper
