# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 30 - 34 of 165

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## Question number: 30

» Numerical Analysis » Interpolation Formulae » Lagrange

Appeared in Year: 2013

### Describe in Detail

Use Simpson’s one-third rule to estimate approximately the area of the cross section of a river 80 feet wide, the depth d (in feet) at a distance x from one bank being given by the following table. :

x | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 |

d | 0 | 4 | 7 | 9 | 12 | 15 | 14 | 8 | 3 |

### Explanation

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## Question number: 31

» Probability » Convergence » In Probability

Appeared in Year: 2011

### Describe in Detail

Let X _{1}, X _{2}, …, X _{n} be a sequence of i. i. d. r. v. s with E (X _{i}) = 0 and V (X _{i}) = 1. Show that the sequence tends to 1 in probability.

### Explanation

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## Question number: 32

» Probability » Bayes' Theorem

Appeared in Year: 2012

### Describe in Detail

The ith box contains 2i white balls and 6 - 2i black balls, i = 1 (1) 3. A fair die is cast once. 3 balls are taken at random from box 1, box 2 or box 3 according as the die shows up face 1, any of 2 and 3, or any of 4, 5 and 6, respectively. Let X denotes the number of white balls drawn. Find E (X).

### Explanation

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## Question number: 33

» Probability » Standard Probability Distributions » Negative Binomial

Appeared in Year: 2012

### Describe in Detail

Items from a large lot are examined one by one until r items with a rare manufacturing defect are found. The proportion of items with this type of defect in the lot is known to be p. Let X denote the number of items needed to be examined. Derive the probability distribution of X, and find E (X).

### Explanation

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## Question number: 34

Appeared in Year: 2011

### Describe in Detail

Let (X, Y) have a bivariate distribution with finite moments upto order 2. Show that

(i) E (E (X|Y) ) =E (X)

(ii) V (X) ≥ V (X|Y)

### Explanation

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