$1.$ Let's assume that you are building a model to detect fraudulent transactions in an online payment system. The priority is to avoid blocking legitimate transactions. Here the number of true positives is $40,$ false positives are $10,$ the true negative is $140$ and false negatives are $10.$ Calculate the precision, recall, and F$1$ score. Now if you have a chance to improve either precision or recall then which one will you choose to improve? Explain your choice

$2.$ Consider the following "dataset" with a single feature $\backslash ($ x $\backslash ),$ and corresponding true label values $\backslash ($ y $\backslash )$ are shown in the table below

a$)$ Write an equation to explain the relationship between $\backslash ($ x $\backslash )$ and $\backslash ($ y $\backslash )$

b$)$ Find the updated value of $\backslash ($ m $\backslash )$ and $\backslash ($ c $\backslash )$ up to the second iteration. $[$ Assume the avg line and its corresponding $\backslash ($ m $\backslash )$ and $\backslash ($ c $\backslash )$ as the first iteration value. Assume that the learning rate $\backslash (=0\mathrm{.}01\backslash ).$ Use MSE as your cost function here$]$

c$)$ Find the final predicted value $\backslash ($ y$\_\{-\}\backslash )$hat for this dataset after $\backslash (2^\{\backslash$text $\{$no $\}\}\backslash )$ iteration

d$)$ Compute the RMSE between the final predicted values obtained in $($b$)$ and true label values, showing all work.

$3.$ If $\backslash (\backslash$mathrm$\{$SS$\}\_\{\backslash$mathrm$\{$fit$\}\}=60\backslash )$ and $\backslash (\backslash$mathrm$\{$SS$\}\_\{\backslash$text $\{$mean $\}\}=80\backslash )$ then find out the corresponding R $2$ score. If another line has $\backslash (\backslash$mathrm$\{$SS$\}\_\{\backslash$mathrm$\{$fit$\}\}=\backslash )50$ then which line is better and why.

$4.$ Suppose you want to teach a robot to grasp objects, navigate through environments, or perform assembly tasks. You also want it to adopt to the changing situations of the environment with time. What kind of learning problems should you use to solve this machine learning problem. Explain your choice. $5.$ Explain the relationship between the learning rate and the convergence of a linear regression model using gradient descent. How does the choice of learning rate impact the training process, and what are the potential consequences of selecting a learning rate that is too small or too large?

$6.$ What are hyperparameters and normalization in a machine learning model.

$7.$ Explain the significance of a negative correlation coefficient in the context of a correlation matrix.

$8.$ What is SMOTE? Explain with examples.