Lab 4 Solution

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Description

  1. 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

p(xjkid) = [0:1; 0:1; 0:1; 0:1; 0:1; 0:1; 0:1; 0:1; 0:1; 0:1]

and

p(xjadult) = [0:02; 0:02; 0:02; 0:02; 0:02; 0:18; 0:18; 0:18; 0:18; 0:18]

(a)

Implement an environment called village that produces a random person in this village,

i.e., it gives out the two tuple (kid/adult,height). Query the environment for say n = 100,

1000 times and then show the histograms for age, height, height given age.

[25]

  1. 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

Bayes Rule.

[15]

  1. 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

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]

  1. 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

(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]

  1. Repeat Q 2.2, with two attributes namely height and weight, i.e., x = (x1; x2), where x1 denotes height and x2 denotes weight.

p(x kid) =

1

e

2

x

1 1111

2

1

e

2

x

2 1212

2

j

p

1

p

1

2 11

2 12

and

1

1 2121

2

1

2 2222

2

p(x adult) =

e

2

x

e

2

x

j

p

1

p

1

2 21

2 22

[20]

End of paper


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