# ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern): Questions 35 - 39 of 39

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## Question number: 35

» Estimation » Optimal Properties » Complete Statistics

Appeared in Year: 2015

### Describe in Detail

Let X _{1}, X _{2}, … X _{n } be a random sample from the binomial distribution with probability mass function

Examine whether the statistic is complete for this distribution.

### Explanation

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## Question number: 36

» Multivariate Analysis » Multivariate Normal Distribution » Mutliple Correlation Coefficient

Appeared in Year: 2015

### Describe in Detail

Let __X__ _{1}, __X__ _{2}, …, __X__ _{n} be a random sample from an population with , a positive definite matrix. Derive 100 (1-α) % simultaneous confidence interval for for all .

### Explanation

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## Question number: 37

» 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

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## Question number: 38

» Hypotheses Testing » Uniformly Most Powerful Test

Appeared in Year: 2015

### Describe in Detail

Fins a Most powerful test for testing the simple hypothesis against the simple alternative hypothesis based on n random observations from N (µ, σ ^{2}) where µ is know. Show that this MP test is UMP (Uniformly most powerful).

### Explanation

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## Question number: 39

» 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

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