Q$.4$ It has been estimated that your best friend wakes up early in the morning $80\%$ of the time.

Whenever he wakes up early, he manages to catch the point bus with a probability of $0\mathrm{.}85.$

However, there is a $5\%$ chance of availing the point bus in the morning in case he wakes up late.

He can always make it to the class at $8$:$30$ if he commutes by point bus. If he misses the point bus,

he is likely to miss the class at $8$:$30$ with a probability of $0\mathrm{.}90.$

a$)$ Draw a Bayesian network to model this problem. Please do remember to include probability

table with each node. $[2]$

b$)$ Caleulate the chance that he wakes up early, misses the point bus but still makes it to the class

at $8$:$30.[4]$

$0\mathrm{.}5$ As the final exams are almost around the corner, you have started skipping physical trainings at

$[$CLO$-2,$ C$3]$

fitness center. When you are busy with studies, you skip the gym $90\%$ of the time. However, you

may also skip the gym when you are not studying but this happens $10\%$ of the time. When you

study on a given day, there is $90\%$ chance that you will study the following day as well. However,

two consecutive days without studies never occur $($you are so much passionate about your

education$).$ Assume $20\%$ chances of skipping studies on ${31}^E$ Jan.

a$)$ Construct an HMM to model the problem. Studying on a day should be taken as the state and

absence from the gym as the evidence. $[2]$

b$)$ Calculate the probability of studying on Feb $3$ if the gym instructor noticed your absence on

$2^{at}$ and $3^{rt}$ February but you attended the gym on $1^{nt}$ February. $[8]$

Note that state estimation is carried out using:

$P(x_{t+1}|e_{1\text{:}t+1})=P(x_{t+1}|e_{1\text{:}t})P(e_{t+1}|x_{t+1})$

$P(x_{t+1}|e_{1\text{:}t})={\displaystyle \underset{x_t}{\overset{?}{}}}P(x_{t+1}|x_t)P(x_t|e_{1\text{:}t})$

Q$.6$ a$)$ Apply $5-$NN algorithm to predict the classes of records $7$ and $8$ in the Table given below. Mention

all the steps clearly. $[4]$

Q$.6$ b$)$ Use perceptron model to discover the weights and bias of two input NOR function with bipolar

inputs and targets. Diseover the response of the network by using each of the training inputs. Draw

$[$CLO$-2,$ C$3]$

Q$.6c)$

the line separating the regions after finding its equation. Assume the learning rate to be I. $[4]$

Use adaline model to discover the weights and bias of two input NAND function with bipolar

inputs and targets in single epoch. Assume the initial weights and bias to be $0\mathrm{.}1$ and the learning

rate to be $0\mathrm{.}2.$ Test the trained network by using each of the training inputs. $[4]$

Q$.6d$ Construct $C4\mathrm{.}5$ decision tree for the dataset shown in the following Table. Mention all the steps

$[$CLO$-2,$ C$3]$

clearly. Generate the decision rules from the developed tree. $[5]$

Q$.7$ a$)$ Outline the strategy to prevent overfitting in decision trees. $[1]$

Q$.7$ b$)$ Examine the impact of choosing an odd value of $k$ in $kNN$ implementation for binary and

multiclass domains. $[1]$

$[$CLO$-1,$ C$3]$

$[$CLO$-1$; C$3]$

Q$.7$ e$)$ Outline the reasons to use machine learning$-[1]$

$[$CLO$-1,$ C$3]$