Multivariate MCQs – 1

Multiple Choice Questions about Multivariate and Multivariate Analysis

1. Let $A$ be a $k\times k$ symmetric matrix and $X$ be a $k\times 1$ vector. Then


2. If $A$ is a square matrix, then $det(A – \lambda)=0$ is known as


3. A square matrix $A$ and its transpose have the Eigenvalues


4. Eigenvalue often introduced in the context of


5. Let $x_1, x_2, \cdots, x_n$ be a random sample from a joint distribution with mean vector $\mu$ and covariance $\sigma$. Then $\overline{x}$ is an unbiased estimator of $\mu$ and its covariance matrix is:


6. A set of vectors $X_1, X_2, \cdots, X_n$ are linearly independent if


7. The pdf of multivariate normal distribution exists only when $\sigma$ is


8. Length of vector $\underline{X}$ is calculated as


9. The set of all linear combination of $X_1, X_2, \cdots, X_k$ is called


10. Eigenvalue is the factor by which the Eigenvector is


11. Let $x_1, x_2, \cdots, x_n$ be a random sample of size $n$ from a p-variate normal distribution with mean $\mu$ and covariance matrix $\sigma$, then


12. Let $x$ be distributed as $N_p(\mu, \sigma)$ with $|\sigma | > 0$, then $(x-\mu)’ \sigma^{-1} (x-\mu)$ is distributed as:


13. If $A$ and $B$ are two $n \times n$ matrices, which of the following is not always true?


14. If $A$ is a square matrix of order ($m \times m$) then the sum of diagonal elements is called


15. Eigenvalues and Eigenvectors are only for the matrices


16. How many Eigenvalues does a 2 by 2 matrix have?


17. What are Eigenvalues?


18. A matrix in which number of rows and columns are equal, is called


19. The rank of a matrix $\begin{bmatrix}1 & 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 1 & 2 \\ 1 & 1 & 0 & 0 & 2 \\ 0 & 1 & 1 & 1 & 3\end{bmatrix}$ is


20. A matrix $A_{m\times n}$ is defined to be orthogonal if\choice{$A’A=I$}{$A^{-1}=A’I$}{$A’A = AA’=I$}{All given Options}{d}{}


Muhammad Imdad Ullah

Currently working as Assistant Professor of Statistics in Ghazi University, Dera Ghazi Khan. Completed my Ph.D. in Statistics from the Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan. l like Applied Statistics, Mathematics, and Statistical Computing. Statistical and Mathematical software used is SAS, STATA, Python, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel. Like to use type-setting LaTeX for composing Articles, thesis, etc.

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