Recent questions tagged statistics

Q.49 Which of the following statements is/are true? (A) If $ A $ is a $ 3 \times 3 $ real matrix with 3 distinct eigenvalues, then $ A $ is diagonalizable. (B) If $...

Q.30 Let $ A $ be a $ 2 \times 2 $ real matrix such that $ AB = BA $ for all $ 2 \times 2 $ real matrices $ B $. If trace of $ A $ equals 5, then determinant of $ A $ (r...

Consider the following statements. (I) Let $ A $ and $ B $ be two $ n \times n $ real matrices. If $ B $ is invertible, then $ \mathrm{rank}(BA) = \mathrm{rank}(A) $. ...

Standard deviation ( $\mathrm{S}$) and coefficient of Variation (CV Expressed as a percentage) of different datasets are given in $\mathrm{A - D}$, below. Compute the mea...

Identify the variables associated with interval scale of measurement:Time of the day in $24$-hour formatDate of birthWeightHeightChoose the correct answer from the option...

Match the $\textbf{List - I}$ with $\textbf{List - II}.$LIST-I(Population Mean $(\mu)$ and $\frac{1}{N} \sum x_{i}^{2}$ )LIST-I(Population Standard Deviation $(\sigma)$ )...

  Let $A$ be the $2 \times 2$ real matrix having eigenvalues $1$ and $-1$, with corresponding eigenvectors $\begin{bmatrix} \frac{\sqrt{3}}{2} \\ \frac{1}{2} \end{bmatrix...

Let $A$ be a $3 \times 3$ real matrix such that $I_3 + A$ is invertible and let $B = (I_3 + A)^{-1}(I_3 - A)$, where $I_3$ denotes the $3 \times 3$ identity matrix. Then ...

The dimension of the vector space of $7 \times 7$ real symmetric matrices with trace zero and the sum of the off-diagonal elements zero is (A) 47 (B) 28 (C) 27 ...

Let $I$ be the $4 \times 4$ identity matrix and $v = (1, 2, 3, 4)^t$, where $t$ denotes the transpose. Then the determinant of $I + vv^t$ is equal to = ?

A prominent newspaper conducted a survey among a carefully chosen sample of $1,00,000$ voters under the age of $25$. A randomly chosen subset of $60 \%$ of this sample we...

The mean and variance of a data set of size $n \geq 100$ are $1.1$ and $4.3$ respectively. It was then discovered that one data point was wrongly recorded as $-0.9$ and s...

​​​​​Let the minimum, maximum, mean and standard deviation values for the attribute income of data scientists be ₹$46000$, ₹ $170000$, ₹ $96000$, and ₹ $21000$, respectiv...

Let $x$ and $y$ be random variables, not necessarily independent, that take real values in the interval $[0,1]$. Let $z=x y$ and let the mean values of $x, y, z$ be $\bar...

Consider the following sample of numbers:$9,18,11,14,15,17,10,69,11,13$The median of the sample is$13.5$$14$$11$$18.7$

Consider two random variables, $x$ and $y$, defined as follows:\[x =\begin{cases}1 & \text{if HH } \\0 & \text{otherwise}\end{cases}\]\[y =\begin{cases}1 & \text{if at le...

You have a single hidden-layer neural network for a binary classification task. The input is \(X \in \mathbb{R}^{n \times m}\), output \(\hat{y} \in \mathbb{R}^{1 \times ...

What is Error Analysis?(i) The process of analyzing the performance of a model through metrics such as precision, recall or F1-score.(ii) The process of scanning mis-clas...