# Multivariate Analysis (ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern)): Questions 7 - 8 of 8

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## Question number: 7

» Multivariate Analysis » Principal Components » Correlations

Appeared in Year: 2015

### Describe in Detail

Let

Determine

(i) The principal components y _{1}, y _{2} and y _{3}.

(ii) The proportion of variance explained each one of them.

(iii) Correlation between the first principal components y _{1} and the third original random variable.

### Explanation

First find the eigen value and eigen vector pairs

To solve this equation, we get the eigen values is

The corresponding eigen vector for each eigen value is by using normalize the eigen vector by the equation

For λ _{1} =6,

## Question number: 8

» Multivariate Analysis » Wishart's Distribution » Reproductive Properties

Appeared in Year: 2015

### Describe in Detail

(i) Let A _{i} be distributed as Wishart , i = 1, 2 and A _{1}, A _{2} be independent. Show that A _{1} +A _{2} is distributed as .

(ii) If A is distributed as , then CAC’ is distributed as where C is a nonsingular matrix of order m.

### Explanation

(i) We have that is

where ) and Y _{i} ’s are independent.

Similarly, that is

where ) and Z _{i} ’s are independent.

We know that A _{1}, A _{2} are independent. So, Y _{i} ’s are independent of Z _{i} ’s