# ISS Statistics Paper I (Old Subjective Pattern): Questions 100 - 104 of 165

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## Question number: 100

Appeared in Year: 2013

Essay Question▾

### Describe in Detail

Out of 200 persons appeared for an examination, 80 % were males and the rest were females. Among 30 married males, 14 were successful; 110 unmarried males were successful. In respect of 10 married females, 4 were successful; 20 unmarried females were successful. Compute Yule’s coefficient of association between success in the examination and the marital status for males as well as females.

### Explanation

Out of 200 persons appeared for an examination, 160 males and 40 are females.

The frequencies for various attributes be show in this contingency table

 Male Successful (A) unsuccessful (a) married (B) (AB) =14 (aB) =16 unmarried (b) (Ab) =110 (ab) =20
 Female successful (A) unsuccessful (a) married (B) (AB)… (70 more words) …

## Question number: 101

» Probability » Convergence » In Distribution

Appeared in Year: 2014

Essay Question▾

### Describe in Detail

{X n} is a sequence of independent variables. Show that

where X is a random variable. Is the converse true?

### Explanation

The sequence X n converges to X in probability if for any ε > 0

The sequence X n converges to the distribution of X as n tends to infinity if

For ε > 0,

Hence

……… (1)

Note that

…. (2)

From… (42 more words) …

## Question number: 102

» Statistical Methods » Bivariate Distributions » Bivariate Normal Distribution

Appeared in Year: 2009

Essay Question▾

### 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

The first integral is

So, the marginal distribution of X 2 is

The mean of X 1 is… (10 more words) …

## Question number: 103

» Statistical Methods » Non-Parametric Test » Wilcoxon

Appeared in Year: 2011

Essay Question▾

### 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… (180 more words) …

## Question number: 104

» Probability » Distribution Function » Standard Probability Distributions

Appeared in Year: 2010

Essay Question▾

### 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)

f Page