GATE Data Science and Artificial Intelligence Practice Quiz

Question 1

Let $X$ be a continuous random variable with probability density function $f_X(x)=2x$, for $0\le x\le 1$, and $0$ otherwise. What is $\mathbb{E}[X]$?

Accepted Answer

$\frac{2}{3}$

Question 2

For a binary classifier, the confusion matrix entries are: true positives $TP=40$, false positives $FP=10$, true negatives $TN=30$, and false negatives $FN=20$. What is the $F_1$-score?

Accepted Answer

$\frac{8}{11}$

Question 3

Consider the matrix $A=\begin{bmatrix}2&0\0&3\end{bmatrix}$. Which of the following are eigenvalues of $A$?

Accepted Answer

$2$

Question 4

A logistic regression model for binary classification uses $p(y=1\mid x)=\sigma(w^Tx+b)$, where $\sigma(z)=\frac{1}{1+e^{-z}}$. Which statements are correct?

Accepted Answer

The decision boundary at threshold $0.5$ is linear in $x$.

Question 5

Suppose $X\in\mathbb{R}^{n\times d}$ has full column rank and the linear regression model is fit by ordinary least squares. The estimator is $\hat{\beta}=(X^TX)^{-1}X^Ty$. Which statement is correct?

Accepted Answer

The residual vector $r=y-X\hat{\beta}$ is orthogonal to every column of $X$.

Practice Quizzes

GATE Data Science and Artificial Intelligence Practice Quiz