Let $C_1$ and $C_2$ be two sets of objects. Let $D(x, y)$ be a measure of dissimilarity between two objects $x$ and $y$. Consider the following definitions of dissimilarity between $C_1$ and $C_2$.

DIS-1 $\left(C_1, C_2\right)=\max _{x \in C_1, y \in C_2} D(x, y)$ DIS-2 $\left(C_1, C_2\right)=\min _{x \in C_1, y \in C_2} D(x, y)$

Which of the following statements Which of the following statements is/are correct?

Given data $\{(-1,1),(2,-5),(3,5)\}$ of the form $(x, y)$, we fit a model $y=w x$ using linear least-squares regression. The optimal value of $w$ is _________

(Round off to three decimal places)

The naive Bayes classifier is used to solve a two-class classification problem with class labels $y_1, y_2$. Suppose the prior probabilities are $P\left(y_1\right)=\frac{1}{3}$ and $P\left(y_2\right)=\frac{2}{3}$. Assuming a discrete feature space with $P\left(x \mid y_1\right)=\frac{3}{4}$ and $P\left(x \mid y_2\right)=\frac{1}{4}$ for a specific feature vector $x$. The probability of misclassifying $x$ is

_________ (Round off to two decimal places)

Let $\left\{x_1, x_2, \ldots ., x_n\right\}$ be a set of linearly independent vectors in $\mathbb{R}^n$. Let the $(\mathrm{i}, \mathrm{j})$ - th element of matrix $A \in \mathbb{R}^{n \times n}$ be given by $A_{i j}=x_i^T x_j, 1 \leq i, j \leq n$. Which one of the following statements is correct?