# ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern): Questions 20 - 25 of 39

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## Question number: 20

» Estimation » Estimation Methods » Maximum Likelihood

Appeared in Year: 2014

### Describe in Detail

Let X be exponentially distributed with parameter θ. Obtain MLE of θ based on a sample of size n, from the above distribution.

### Explanation

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## Question number: 21

» Estimation » Optimal Properties » Confidence Interval Estimation

Appeared in Year: 2015

### Describe in Detail

Let y _{1}, y _{2, …, } y _{n} be a random sample from N (µ, σ ^{2}) where µ and σ ^{2} are both unknown. Obtain a confidence interval of µ with confidence coefficient (1-α)

### Explanation

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## Question number: 22

» Estimation » Optimal Properties » Sufficient Estimator

Appeared in Year: 2015

### Describe in Detail

Obtain the sufficient statistics for the following distribution.

(i)

(ii)

### Explanation

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## Question number: 23

» Multivariate Analysis » Distribution of Hotelling T2 Statistic » Use for Testing

Appeared in Year: 2015

### Describe in Detail

Show that T ^{2} statistic is invariant under changes in the unit of measurements for a p×1 random vector X of the form __Y__ =C __X __ + __d __ where C is a p×p nonsingular matrix, __d__ is a p×1 vector.

### Explanation

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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

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## 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

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