Consider a two-class problem in $R^d$ with class labels red and green. Let $\mu_{\text {red }}$ and $\mu_{\text {green }}$ be the means of the two classes.

Given test sample $x \in R^d$, a classifier calculates

the squared Euclidean distance (denoted by $\|\cdot\|^2$ ) between $x$ and the means of the two classes and assigns the class label that the sample x is closest to. That is, the classifier computes

$$ f(x)=\left\|\mu_{\text {red }}-x\right\|^2-\left\|\mu_{\text {green }}-x\right\|^2 $$

and assigns the label red to $x$ if $f(x)<0$, and green otherwise. Which of the following statements is/are correct?

Let $D=\left\{x^{(1)}, \ldots ., x^{(n)}\right\}$ be a dataset of $n$ observations where each $x^i \in \mathbb{R}^{100}$. It is given that $\sum_{i=1}^n x^{(\mathrm{i})}=0$ The covariance matrix computed from $D$ has eigenvalues $\lambda_i=100^{2-i}, 1 \leq i \leq 100$. Let $u \in \mathbb{R}^{100}$ be the direction of maximum variance with $u^T u=1$.

The value of $\frac{1}{n} \sum_{i=1}^n\left(u^T x^{(i)}\right)^2= $_________

Consider the following Python declarations of two lists.

$$ \begin{aligned} & A=[1,2,3] \\ & B=[4,5,6] \end{aligned} $$

Which one of the following statements results in $A=[1,2,3,4,5,6]$ ?

Consider the following Python code snippet.

$\mathrm{A}=\{$ "this","that" $\}$

$B=\{$ "that","other" $\}$

$\mathrm{C}=\{$ "other","this"}

while "other" in C :

if "this" in A :

$\mathrm{A}, \mathrm{B}, \mathrm{C}=\mathrm{A}-\mathrm{B}, \mathrm{B}-\mathrm{C}, \mathrm{C}-\mathrm{A}$

if "that" in B ;

$\mathrm{A}, \mathrm{B}, \mathrm{C}=\mathrm{C}|\mathrm{A}, \mathrm{A}| \mathrm{B}, \mathrm{B} \mid \mathrm{C}$

When the above program is executed, at the end, which of the following sets contains "this"?