# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 1 - 7 of 165

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## Question number: 1

» Probability » Distribution Function » Standard Probability Distributions

Appeared in Year: 2011

### Describe in Detail

Show that the square of the one sample t-statistic has the F-distribution. What are its degrees of freedom?

### Explanation

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## Question number: 2

» Statistical Methods » Regression » Linear

Appeared in Year: 2011

### Describe in Detail

Show that the best predictor of Y, in terms of minimum MSE, is linear in X, if (X, Y) has bivariate normal distribution.

### Explanation

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## Question number: 3

» Statistical Methods » Tests of Significance » Chi-Square

Appeared in Year: 2013

### Describe in Detail

From along series of annual river flows, the variance is found out to be 49 units. For a new sample of 25 years, the variance is calculated as 81 units. Can we regard that the sample variance is significant? (Given the chi-square value at 5 % level of significance as 37.7)

### Explanation

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## Question number: 4

» Probability » Central Limit Theorems

Appeared in Year: 2013

### Describe in Detail

State and prove Lindeberg-Levy Central limit theorem.

### Explanation

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## Question number: 5

» Probability » Standard Probability Distributions » Normal

Appeared in Year: 2013

### Describe in Detail

If X ~ N (0, 1), obtain the distribution of X ^{2}.

### Explanation

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## Question number: 6

» Statistical Methods » Measures of Location

Appeared in Year: 2010

### Describe in Detail

A cyclist pedals from his house to his college at a speed of l0 km per hour and back from the college to his house at 15 km per hour. Find the average speed.

### Explanation

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## Question number: 7

» Statistical Methods » Non-Parametric Test » Wald-Wolfowitz

Appeared in Year: 2011

### Describe in Detail

Explain the Wald-Wolfowitz run test for randomness in a sequence of two types of symbols. Find E _{Ho} (R) where R denotes the number of runs of elements of one kind.

### Explanation

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