List of top Statistics Questions asked in CPET

In a central difference table, which of the following is correct?

Consider the Assertion (A) and Reason (R) given below:
Assertion (A): \(\displaystyle\int_0^t \sin x\, dx = 1 - \cos t\)
Reason (R): \(\sin x\) is continuous in any closed interval \([0, t]\).

The series \(\dfrac{1}{2} - \dfrac{2}{3}\cdot\dfrac{1}{2^3} + \dfrac{3}{4}\cdot\dfrac{1}{3^3} - \dfrac{4}{5}\cdot\dfrac{1}{4^3} + \cdots\) is:

If \(A\) is a \(3\times 3\) matrix and \(B\) is its adjoint matrix, the determinant of \(B\) is \(64\), then what is the determinant of \(A\)?

If \(A = \begin{bmatrix} 5 & 0 & -2 \\ 0 & 1 & 0 \\ -4 & 0 & -1 \end{bmatrix}\) and \(I\) is the \(3 \times 3\) unit matrix, then the rank of \(I - A\) is:

The function \(f(x) = x^5 - 5x^4 + 5x^3 - 1\) has:

Read the following statements and find out which of these statements is/are correct:

I. If \(\alpha, \beta, \gamma\) are three linearly independent vectors in \(V(F)\) then \(\alpha+\beta\), \(\beta+\gamma\) and \(\gamma+\alpha\) are also linearly independent.

II. The vectors \(2x^3+x^2+x+1,\ x^3+3x^2+x-2,\ x^3+2x^2-x+3\) of \(V_4(R)\) are linearly independent.

The value of \[\begin{vmatrix} a+pd & a+qd & a+rd \\ p & q & r \\ d & d & d \end{vmatrix}\] is:

For real numbers x and y, we write \(xRy \iff x - y + \sqrt{2}\) is an irrational number. Then the relation R is:

The second derivative of \(f(\log x)\) where \(f(x) = \log x\) is:

Consider a Markov Chain with state space \(S = \{0, 1\}\) and the transition probability matrix \(P = \begin{pmatrix} 1 & 0 \\ 0.5 & 0.5 \end{pmatrix}\). What is the value of \(P^{(2)}_{10}\)?

A square matrix with non-negative elements and unit row sums is called as a:

Which of the following statements is incorrect?

The derivative of \(\dfrac{1}{\sin x}\) with respect to \(\cos x\) is:

Given that \(X=(X_1\ X_2\ X_3)' \sim N_3(\mu,\Sigma)\), where \(\mu=(0\ 0\ 0)'\) and \(\Sigma=\begin{pmatrix}1 & 1 & 0\\1 & 4 & 1\\0 & 1 & 4\end{pmatrix}\). The correlation coefficient between \(X_2\) and \(X_3\) is given by:

If \(A\) is a \(3\times 3\) non-zero matrix such that \(A^2=0\), then the number of non-zero eigen values of \(A\) is:

Given that \(X=(X_1\ X_2\ X_3)' \sim N_3(\mu, \Sigma)\), where \(\mu=(0\ 0\ 0)'\) and \(\Sigma = \begin{pmatrix}1 & 0 & 0\\0 & 4 & -1\\0 & -1 & 1\end{pmatrix}\).
Which of the following is true?

Consider a Markov Chain with transition probability matrix \(P = \begin{pmatrix}0 & 1 & 0\\0.5 & 0 & 0.5\\0 & 1 & 0\end{pmatrix}\) with state space \(S=\{0,1,2\}\). Then:

Which of the following is essential for completely specifying a Markov Chain?

Given that \(X \sim N_3(\mu_1, \Sigma)\), where \(\mu_1 = (0\ 1\ 0)'\) and \(Y \sim N_3(\mu_2, \Sigma)\), where \(\mu_2 = (0\ -1\ 0)'\), then which of the following statements are true?
Statement 1: \((X+Y)^2\) has a central Chi-square distribution.
Statement 2: \((X-1)^2 + (Y+1)^2\) has a central Chi-square distribution.

A population having constant size and composition is called a:

Standardized death rates are particularly useful for:

The death rate of women due to delivery of babies is termed as:

Fertility rates mainly depend on:

The probability \(q_x\) of dying of a person between the age interval \(x\) and \((x+1)\), and the central mortality rate \(m_x\) are related as: