Description

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] 

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]

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]

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) = ^{p}_{2} _{1} e
2
_{1}
2
and p(x adult) =
^{p}2 _{2} ^{e}
2
_{2}
2
are
j
1
1
x _{1}
j
1
1
x _{2}
both onedimensional Gaussian random variables.
[10]

Repeat Q 2.2, with two attributes namely height and weight, i.e., x = (x_{1}; x_{2}), where x_{1} denotes height and x_{2} denotes weight.
p(x kid) = 
1 
e 
2 
x 
1 _{11}11 
2 
1 
e 
2 
x 
2 _{12}12 
2 

j 
p 
1 
p 
1 

2 _{11} 
2 _{12} 

and 
1 
1 _{21}21 
2 
1 
2 _{22}22 
2 

p(x adult) = 
e 
2 
x 
e 
2 
x 

j 
p 
1 
p 
1 

2 _{21} 
2 _{22} 
[20]
End of paper