# ISS Statistics Paper II (Old Subjective Pattern): Questions 24 - 28 of 39

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## Question number: 24

» Statistical Quality Control » Concepts of ATI

Appeared in Year: 2015

### Describe in Detail

For a sequential probability ratio test of strength (α, β) and stopping bounds are A and B (B < A), show that A ≤ 1-β/α and B ≥ β/1-α

### Explanation

Let X= (X _{1}, …, X _{k}) and also let E _{k} be the set of all points in k dimensional Euclidean space R _{k}, for which we reject H _{0} using the sequential probability ratio test. Also, let F _{k } be the set of all points… (315 more words) …

## Question number: 25

» Multivariate Analysis » Multivariate Normal Distribution » Mutliple Correlation Coefficient

Appeared in Year: 2015

### Describe in Detail

Let X= (X _{1}, X _{2}, X _{3}) ’ be distributed as N _{3} (µ, ∑) where µ’= (2, -3, 1) and

(i) Find the distribution of 3X _{1} -2X _{2} +X _{3}.

(ii) Find a 2 × 1 vector a such that X _{2} and are independent.

### Explanation

(i) the distribution of 3X _{1} -2X _{2} +X _{3} is

The mean is

… (302 more words) …

## Question number: 26

» Statistical Quality Control » Sequential Sampling Plans

Appeared in Year: 2015

### Describe in Detail

To test the hypothesis against for the distribution

Develop the sequential probability ratio test.

### Explanation

Let x _{1}, x _{2}, …, x _{n} are independently and identically distributed with distribution is

Let type I and type II errors… (502 more words) …

## Question number: 27

» Multivariate Analysis » Multivariate Normal Distribution » Partial Correlation Coefficient

Appeared in Year: 2015

### Describe in Detail

Let __X__ = (X _{1}, X _{2}, X _{3}) ’ be distributed as N _{3} (__µ__, ∑) where __ µ__ = (10, -7, 2) ’ and

Find the partial correlation between X _{1} and X _{2} given X _{3}.

### Explanation

The partial correlation between X _{1} and X _{2} given X _{3} is defined as

where these… (175 more words) …

## Question number: 28

» 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

… (206 more words) …