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

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Question number: 100

» Statistical Methods » Association and Contingency

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

Equation

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

Equation

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

Equation

For ε > 0,

Equation

Equation

Hence

Equation ……… (1)

Note that

Equation

Equation …. (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),

Equation

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

Explanation

The joint density is written as

Equation

The marginal distribution of X 1

Equation

Equation

Equation

Equation

Equation

Equation

The marginal distribution of X 2 is

Equation

Equation

Equation

The first integral is

Equation

Equation

So, the marginal distribution of X 2 is

Equation

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

Equation

Obtain P (X > 0.3).

Explanation

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

Equation

Equation

Equation

Equation

Equation

So, density is

Equation

Then obtain P (X > 0.3)

Equation

Equation

Equation

Equation

Equation

Equation

Equation

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