IGNOU MST 18 SOLVED ASSIGNMENT

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IGNOU MST 18 SOLVED ASSIGNMENT

~~Rs. 400~~
Rs. 205

IGNOU MST 18 SOLVED ASSIGNMENT

~~Rs. 400~~
Rs. 205

Last Date of Submission of IGNOU MST-018 (MSCAST) 2025 Assignment is for January 2025 Session: 30th September, 2025 (for December 2025 Term End Exam).
Semester Wise
January 2025 Session: 30th March, 2025 (for June 2025 Term End Exam).
July 2025 Session: 30th September, 2025 (for December 2025 Term End Exam).

Title Name	IGNOU MST 18 SOLVED ASSIGNMENT
Type	Soft Copy (E-Assignment) .pdf
University	IGNOU
Degree	MASTER DEGREE PROGRAMMES
Course Code	MSCAST
Course Name	M.Sc. (Applied Statistics)
Subject Code	MST 18
Subject Name	Multivariate Analysis
Year	2025
Session
Language	English Medium
Assignment Code	MST-018/Assignmentt-1//2025
Product Description	Assignment of MSCAST (M.Sc. (Applied Statistics)) 2025. Latest MST 018 2025 Solved Assignment Solutions
Last Date of IGNOU Assignment Submission	Last Date of Submission of IGNOU MST-018 (MSCAST) 2025 Assignment is for January 2025 Session: 30th September, 2025 (for December 2025 Term End Exam). Semester Wise January 2025 Session: 30th March, 2025 (for June 2025 Term End Exam). July 2025 Session: 30th September, 2025 (for December 2025 Term End Exam).

~~Rs. 400~~
Rs. 205

Questions Included in this Help Book

Ques 1.

State whether the following statements are true or false and also give the reason in support of your answer:

(a) The covariance matrix of random vectors $\underline{X}\text{and}\underline{Y}$ is symmetric.

(b) $if\underline{x}$ is a p-variate normal random vector, then every linear combination $\underline{c{}'}$ $\underline{x}$ is a scalar vector, is also p-variate normal vector

(d) If a matrix is positive definite then its inverse is also positive definite.

(e) $\text{If}\underline{X}\sim N_2\left(\begin{pmatrix}2\\1\end{pmatrix},\begin{pmatrix}1&0\\0&1\end{pmatrix}\right)\text{and}\underline{Y}\sim N_2\left(\begin{pmatrix}-1\\3\end{pmatrix},\begin{pmatrix}1&0\\0&1\end{pmatrix}\right),\text{then}$

$\underline{X}+\underline{Y}\sim N_2\left(\begin{pmatrix}1\\4\end{pmatrix},\begin{pmatrix}2&0\\0&2\end{pmatrix}\right).$

Ques 2.

$\text{Let}\underline{X}=\begin{pmatrix}X_1\\X_2\end{pmatrix}$ has the following joint density function

$f(x_1,x_2)=\begin{cases}4x_1x_2&,0<x_1<1,0<x_2<1\\0&,\text{otherwise}.\end{cases}$

Find the marginal distributions, mean vector and variance-covariance matrix. Also, comment on the independence of X₁and X₂

Ques 3.

) $\underline{X}=\begin{pmatrix}\underline{X}^{(1)}\\\underline{X}^{(2)}\end{pmatrix}\sim N_4(\underline{\mu},\underline{\Sigma})$ whare $\underline{\mu}=\begin{pmatrix}-4\\1\\4\\0\end{pmatrix},\quad\underline{\Sigma}=\begin{pmatrix}2&2&|&3&0\\2&1&|&2&0\\--&--&--&--&--\\3&2&|&2&1\\0&0&|&1&1\end{pmatrix}$ Find the

$E(\underline{X}^{(2)}|\underline{X}^{(1)}=\underline{x}^{(1)})\quad\text{and}\quad Cov(\underline{X}^{(2)}|\underline{X}^{(1)}=\underline{x}^{(1)})$

Ques 4.

Let X  be a 3-dimensional random vector with dispersion matrix

$\underline{\Sigma}=\begin{pmatrix}4&-2&0\\-2&4&0\\0&0&2\end{pmatrix}$

Determine the first principal component and the proportion of the total variability that it explains.

Ques 5.

) $\underline{X}\sim N_4(\underline{\mu},\underline{\Sigma}),\quad\text{where}\quad\underline{\mu}=\begin{pmatrix}3\\-2\\1\\-2\end{pmatrix}$ and $\underline{\Sigma}=\begin{pmatrix}4&0&0&0\\0&3&0&0\\0&0&2&-2\\0&0&-2&5\end{pmatrix}$ Check the

independence $\text{of the(i)}X_2\text{and}X_1\quad\text{(ii)}(X_2,X_4)\text{and}(X_1,X_3)\quad\text{(iii)}(X_1,X_2)\text{and}(X_3,X_4)$

Ques 6.

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 vector $\underline{x}=\begin{pmatrix}x_1\\x_2\\x_3\\x_4\end{pmatrix}\quad\text{and}\quad\underline{y}=\begin{pmatrix}y_1\\y_2\\y_3\\y_4\end{pmatrix}$ then obtain the sample covariance matrix between $\underline{x}\text{and}\underline{y}$

Source: Anscombe, Francis J. (1973). Graphs in statistical analysis. The American Statistician, 27, 17– 21. doi: 10.2307/2682899.

Ques 7.

Obtain the maximum likelihood estimator of the mean vector and variance-covariance matrix of the multivariate normal distribution.

Ques 8.

Covariance Matrix

Ques 9.

Mahalanobis D2

Ques 10.

Hotelling’s T2

Ques 11.

Clustering

Ques 12.

Relationship between (ii) and (iii).

Ques 13.

$\text{If}\underline{X}\sim N_3(\underline{\mu},\underline{\Sigma})\text{with}\underline{\mu}=\begin{pmatrix}2\\1\\2\end{pmatrix}\text{and}\underline{\Sigma}=\begin{pmatrix}5&3&0\\3&3&-2\\0&-2&5\end{pmatrix}.$ Then find the joint distribution of $X_1+2X_2,\quad 2X_1-X_2\quad\text{and}\quad X_3.$

Ques 14.

State whether the following statements are true or false and also give the reason in support of your answer:

(a) The covariance matrix of random vectors $\underline{X}\text{and}\underline{Y}$ is symmetric.

(b) $if\underline{x}$ is a p-variate normal random vector, then every linear combination $\underline{c{}'}$ $\underline{x}$ is a scalar vector, is also p-variate normal vector

(d) If a matrix is positive definite then its inverse is also positive definite.

$\underline{X}+\underline{Y}\sim N_2\left(\begin{pmatrix}1\\4\end{pmatrix},\begin{pmatrix}2&0\\0&2\end{pmatrix}\right).$

Ques 15.

$\text{Let}\underline{X}=\begin{pmatrix}X_1\\X_2\end{pmatrix}$ has the following joint density function

$f(x_1,x_2)=\begin{cases}4x_1x_2&,0<x_1<1,0<x_2<1\\0&,\text{otherwise}.\end{cases}$

Find the marginal distributions, mean vector and variance-covariance matrix. Also, comment on the independence of X₁and X₂

Ques 16.

$E(\underline{X}^{(2)}|\underline{X}^{(1)}=\underline{x}^{(1)})\quad\text{and}\quad Cov(\underline{X}^{(2)}|\underline{X}^{(1)}=\underline{x}^{(1)})$

Ques 17.

Let X  be a 3-dimensional random vector with dispersion matrix

$\underline{\Sigma}=\begin{pmatrix}4&-2&0\\-2&4&0\\0&0&2\end{pmatrix}$

Determine the first principal component and the proportion of the total variability that it explains.

Ques 18.

independence $\text{of the(i)}X_2\text{and}X_1\quad\text{(ii)}(X_2,X_4)\text{and}(X_1,X_3)\quad\text{(iii)}(X_1,X_2)\text{and}(X_3,X_4)$

Ques 19.

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

Source: Anscombe, Francis J. (1973). Graphs in statistical analysis. The American Statistician, 27, 17– 21. doi: 10.2307/2682899.

Ques 20.

Obtain the maximum likelihood estimator of the mean vector and variance-covariance matrix of the multivariate normal distribution.

Ques 21.

Covariance Matrix

Ques 22.

Mahalanobis D2

Ques 23.

Hotelling’s T2

Ques 24.

Clustering

Ques 25.

Relationship between (ii) and (iii).

Ques 26.

~~Rs. 400~~
Rs. 205

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Course Name	M.Sc. (Applied Statistics)
Course Code	MSCAST
Programm	MASTER DEGREE PROGRAMMES Courses
Language	English

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