# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 105 - 109 of 165

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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),

## 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

## Question number: 107

» Probability » Tchebycheffs Inequality

Appeared in Year: 2009

### Describe in Detail

Let X ~ BIN (100, 0.2). Compute P [10 ≤ X ≤ 30].

### Explanation

X ~ BIN (100, 0.2), where n = 100, p = 0.2, q = 0.8

E (X) =np = 20, Var (X) =npq = 16, σ = 4

Let X be a random variable with meanE (X) = µ and variance Var (X) = σ ^{2}. Then any

## Question number: 108

» Numerical Analysis » Interpolation Formulae » Lagrange

Appeared in Year: 2010

### Describe in Detail

The following values of the function f (x) for values of x are given:

f (l) = 4, f (2) = 5, f (7) = 5, f (8) = 4.

Find the value of f (6) and also the value of x for which f (x) is maximum or minimum.

### Explanation

This is written in the table in this function y = f (x)

x | 1 | 2 | 7 | 8 |

y | 4 | 5 | 5 | 4 |

For find x = 6, we use Lagrange’s interpolation polynomial because the x values is not equal interval. There are four values of x which gives the

## Question number: 109

» Statistical Methods » Non-Parametric Test » Mann-Whitney

Appeared in Year: 2015

### Describe in Detail

Consider the two samples as follows:

Sample I = 6, 7, 8, 10, 12, 14, 16, 23

Sample II: 9, 11, 13, 15, 17, 18, 19, 20, 24

Test whether the examples have come from the same population by Wilcoxon-Mann-Whitney test at 10 % level of significance. [You can use normal approximation]

### Explanation

Let the sample I consider the population X and sample II consider the population Y. The hypothesis whether two sample comes from same identical population. We test the following null and alternative hypothesis is

In Wilcoxon-Mann-Whitney test, first consider the combined ordered sequence of the sample values is

Sample: