Question
) and
Check the
independence
Answer :
Word Count : 332
We are given: $$ \underline{X} = \begin{pmatrix} X_1 \\ X_2 \\ X_3 \\ X_4 \end{pmatrix} \sim N_4\left( \underline{\mu}, \underline{\Sigma} \right), \quad \text{where} \quad \underline{\mu} = \begin{pmatrix} 3 \\ -2 \\ 1 \\ -2 \end{pmatrix}, \quad \underline{\Sigma} = \begin{pmatrix} 4 & 0 & 0 & 0 \\ 0 & 3 & 0 & 0 \\ 0 & 0 & 2 & -2 \\ 0 & 0 & -2 & 5 \end{pmatrix} $$ --- ### ✦ Key Concept: In a multivariate normal distribution, two components ________ ____ __________ _____ __________ _________ ______ _________.
_____ __________ ______ ______ ______ _________.
______ _____ _______ ___ ______ _________ _____ ______ ____ ________ ________.
_________ ________ _______ ______ _________ ______.
________ _____ ____ ______ ________ _______ ___ ____ ______ ________ ______.
_______ ___ ________ _____ ____ __________ _______ ___.
___ ________ ___ ________ ___ _______ ________ _________ ______ _________.
________ ________ ___ _____ ___ ______ _________ ___ ____ __________.
_______ ____ ______ ___ ________ __________.
____ __________ ___ ______ ____ ______.
_______ ____ ______ ________ ____ _______ __________ ___.
_____ __________ _________ ____ __________ _______ _______.
_________ ________ _________ ______ _________ ____.
_______ _______ _____ _________ _____.
________ ______ _________ _______ _______ _________ ___.
_________ _______ _____ _____ ________ __________.
____ __________ _____ _________ ______ ____ ________ ______ ____.
_________ _____ __________ _______ _____.
_______ _________ _______ _________ _________.
____ ____ __________ _________ ____ ______.
___ _________ ________ _______ ____ ___ ____ ________ __________ _______ _________ ____.
___ _______ _______ ___ ____ __________ _______ ________ ____.
______ _____ ____ __________ __________.
_____ ______ ___ ________ ______ _____ _____ __________ _____ _____.
_________ ______ ______ ________ __________ _________.
____ _____ ___ _______ _________ _____ ______ ___ _________ _________.
____ _______ ____ __________ ____ __________ ____ ______ _________.
_____ ______ ________ __________ ________ ________ _______ _____ ______ __________.
_________ ____ ____ _________ __________ ___ _____ __________ _______ _____.
_________ _______ _____ ____ _____ _______ ________ _________ __________.
__________ ________ _______ _____ ___ ______ ________ _____ ______ __________.
___ _____ ___.
Get Full Answer on WhatsApp
We are given: $$ \underline{X} = \begin{pmatrix} X_1 \\ X_2 \\ X_3 \\ X_4 \end{pmatrix} \sim N_4\left( \underline{\mu}, \underline{\Sigma} \right), \quad \text{where} \quad \underline{\mu} = \begin{pmatrix} 3 \\ -2 \\ 1 \\ -2 \end{pmatrix}, \quad \underline{\Sigma} = \begin{pmatrix} 4 & 0 & 0 & 0 \\ 0 & 3 & 0 & 0 \\ 0 & 0 & 2 & -2 \\ 0 & 0 & -2 & 5 \end{pmatrix} $$ --- ### ✦ Key Concept: In a multivariate normal distribution, two components ________ ____ __________ _____ __________ _________ ______ _________.
_____ __________ ______ ______ ______ _________.
______ _____ _______ ___ ______ _________ _____ ______ ____ ________ ________.
_________ ________ _______ ______ _________ ______.
________ _____ ____ ______ ________ _______ ___ ____ ______ ________ ______.
_______ ___ ________ _____ ____ __________ _______ ___.
___ ________ ___ ________ ___ _______ ________ _________ ______ _________.
________ ________ ___ _____ ___ ______ _________ ___ ____ __________.
_______ ____ ______ ___ ________ __________.
____ __________ ___ ______ ____ ______.
_______ ____ ______ ________ ____ _______ __________ ___.
_____ __________ _________ ____ __________ _______ _______.
_________ ________ _________ ______ _________ ____.
_______ _______ _____ _________ _____.
________ ______ _________ _______ _______ _________ ___.
_________ _______ _____ _____ ________ __________.
____ __________ _____ _________ ______ ____ ________ ______ ____.
_________ _____ __________ _______ _____.
_______ _________ _______ _________ _________.
____ ____ __________ _________ ____ ______.
___ _________ ________ _______ ____ ___ ____ ________ __________ _______ _________ ____.
___ _______ _______ ___ ____ __________ _______ ________ ____.
______ _____ ____ __________ __________.
_____ ______ ___ ________ ______ _____ _____ __________ _____ _____.
_________ ______ ______ ________ __________ _________.
____ _____ ___ _______ _________ _____ ______ ___ _________ _________.
____ _______ ____ __________ ____ __________ ____ ______ _________.
_____ ______ ________ __________ ________ ________ _______ _____ ______ __________.
_________ ____ ____ _________ __________ ___ _____ __________ _______ _____.
_________ _______ _____ ____ _____ _______ ________ _________ __________.
__________ ________ _______ _____ ___ ______ ________ _____ ______ __________.
___ _____ ___.
Get Full Answer on WhatsApp
Related Questions
Consider the following data of 11 samples on 8 variables by Anscombe, Francis J. (1973):
| x1 | x2 | x3 | x4 | y1 | y2 | y3 | y4 |
| 10 | 10 | 10 | 8 | 8.04 | 9.14 | 7.46 | 6.58 |
| 8 | 8 | 8 | 8 | 6.95 | 8.14 | 6.77 | 5.76 |
| 13 | 13 | 13 | 8 | 7.58 | 8.74 | 12.74 | 7.71 |
| 9 | 9 | 9 | 8 | 8.81 | 8.77 | 7.11 | 8.84 |
| 11 | 11 | 11 | 8 | 8.33 | 9.26 | 7.81 | 8.47 |
| 14 | 14 | 14 | 8 | 9.96 | 8.10 | 8.84 | 7.04 |
| 6 | 6 | 6 | 8 | 7.24 | 6.13 | 6.08 | 5.25 |
| 4 | 4 | 4 | 19 | 4.26 | 3.10 | 5.39 | 12.50 |
| 12 | 12 | 12 | 8 | 10.84 | 9.13 | 8.15 | 5.56 |
| 7 | 7 | 7 | 8 | 4.82 | 7.26 | 6.42 | 5.56 |
| 5 | 7 | 5 | 8 | 5.68 | 4.74 | 5.73 | 5.56 |
If the vectorthen obtain the sample covariance matrix between
) whare
Find the
Let X be a 3-dimensional random vector with dispersion matrix
Determine the first principal component and the proportion of the total variability that it explains.
Then find the joint distribution of
Mahalanobis D2
Obtain the maximum likelihood estimator of the mean vector and variance-covariance matrix of the multivariate normal distribution.
Clustering
IGNOU NEWS
Assignment Submission Last Date Extended Till 30 June 2026 Click Here★★★IGNOU June 2026 TEE Date Sheet Released Click Here★★★