# Multivariate Analysis-Estimation (ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern)): Questions 1 - 2 of 2

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## Question number: 1

» Multivariate Analysis » Estimation » Covariance Matrix

Appeared in Year: 2014

### Describe in Detail

Let ,

Find ρ such that X _{1 } +X _{2 } +X _{3 } and X _{1 } -X _{2 } -X _{3 } are independent.

### Explanation

Let

Given that Y and Z are independent, So

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## Question number: 2

» Multivariate Analysis » Estimation » Covariance Matrix

Appeared in Year: 2015

### Describe in Detail

Find the maximum likelihood estimator of the 2×1 mean vector µ and the 2×2 covariance matrix ∑ based on the random sample.

from a bivariate normal distribution.

### Explanation

We known that the maximum likelihood estimator of multivariate normal distribution is

Assume

So,

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