# Statistical Methods (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 1 - 6 of 72

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## Question number: 1

» 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: 2

» 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: 3

» 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: 4

» 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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## Question number: 5

» Statistical Methods » Correlation Coefficient » Multiple Correlation

Appeared in Year: 2009

### Describe in Detail

(i) Show that the arithmetic mean of (positive) regression coefficients is greater than the correlation coefficient.

(ii) What is the value of the product of geometric mean of variances and the geometric mean of regression coefficients?

### Explanation

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## Question number: 6

» Statistical Methods » Regression » Polynomial

Appeared in Year: 2013

### Describe in Detail

Given the two regression lines between X and Y, 2Y -X - 50 = 0, 3Y-2X - 10 = 0, compute the means of X and Y and the correlation coefficient between X and Y.

### Explanation

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