# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 102 - 106 of 165

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## Question number: 102

» Statistical Methods » Bivariate Distributions » Bivariate Normal Distribution

Appeared in Year: 2009

### Describe in Detail

Given the joint density of (X _{1}, X _{2}),

Find the marginal densities of X _{1} and X _{2}. Also find E [X _{1}].

### Explanation

The joint density is written as

The marginal distribution of X _{1}

The marginal distribution of X _{2 } is

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## Question number: 103

» Statistical Methods » Non-Parametric Test » Wilcoxon

Appeared in Year: 2011

### Describe in Detail

Apply the Wilcoxon two-sample test to the following data on the first breakdown times of two brands of computers:

Brand A 98,102,47,85,99,140,130

Brand B 95,125,160,155,148.

Use 1·96 as the critical point for the appropriate test.

### Explanation

Let n _{1} be the number of breakdown times in the Brand A with median time m _{1}, and n _{2} the number of breakdown times in the Brand B with median time m _{2}. Then the hypothesis is that the median times of the two brands are equal against the alternative that they are unequal.

For this first arrange the observations of the combine

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## Question number: 104

» Probability » Distribution Function » Standard Probability Distributions

Appeared in Year: 2010

### Describe in Detail

Let k > 0 be a constant, and

Obtain P (X > 0.3).

### Explanation

We first find the k value for which the f (x) is purely probability density function that is

So, density is

Then obtain P (X > 0.3)

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## Question number: 105

» Probability » Probability of M Events Out of N

Appeared in Year: 2010

### Describe in Detail

A unbaised die is rolled twice. Let A be the event that the first throw shows a number ≤ 2, and B be the event that the second throw shows at least 5. Show that P (AUB) =5/9.

### Explanation

A fair die is rolled twice; the sample space consists of thirty six outcomes. The sample space is

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)

(6,1), (6,2), (6,3), (6,4), (5,5)

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## Question number: 106

» Numerical Analysis » Numerical Integration

Appeared in Year: 2012

### Describe in Detail

The speed y (in km/hr) of a car at different points of time x between 10: 00 a. m. and 10: 40 a. m. on some day was recorded as follows:

Time x (a. m. ) | 10.00 | 10.10 | 10.20 | 10.30 | 10.40 |

Speed y (in km/hr) | 24.2 | 35.0 | 41.3 | 42.8 | 39.2 |

Calculate the approximate distance covered by the car between 10: 00 a. m. and 10: 40 a. m. on that day using Simpson’s one-third formula for numerical integration.

### Explanation

Answer: T he one-third rule of the integrand using Simpson’s rule is

Here n = 4, b = 10: 40 = 40 minutes, a = 10.00 = 0 minutes, h= (b-a) /n = 10 minutes

The distance covered by the car between 10: 00 a. m. and 10: 40 a. m. is

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