ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 147 - 150 of 165

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Question number: 147

» Probability » Probability Generating Functions

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Appeared in Year: 2009

Essay Question▾

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Find the generating function of X whose probability density function is

P [X = r] =pq r-1, r = 1,2, …, 0 < p < 1, q = 1 - p

Explanation

The probability generating function is defined as

Question number: 148

» Statistical Methods » Non-Parametric Test » Wald-Wolfowitz

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Appeared in Year: 2015

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Given the random samples

X: 1,5, 7,9, 15,17,21,23

Y: 2,6, 10,12,18,20,26,28,32

From the populations having the distribution function respectively as F 1 and F 2, test the hypothesis

against

at 5 % level of significance by the Wald-Wolfowitz run test. It is given that the critical number of runs at the sample sizes (8,9) at 5 % level is 5.

Explanation

Wald-Wolfowitz run test uses the data of two random samples, sample 1 is X variables of size n = 8 and sample 2 is Y variables of size m = 9 from two population F 1 (x) and F 2 (y) respectively.

The hypothesis under the test is that the null hypothesis is the two population are identical otherwise the alternative is the population is differ.

… (100 more words) …

Question number: 149

» Statistical Methods » Correlation Coefficient » Partial Correlation

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Appeared in Year: 2010

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Find the most likely price in Mumbai corresponding to the price of Rs. 70 at Kolkata from the following:

Kolkata

Mumbai

Average price

65

67

Standard deviation

2.5

3.5

Correlation coefficient between the prices of commodities in the two cities is 0·8.

Explanation

First we find the regression coefficient β YX where Y is the price at Mumbai and X is the price at Kolkata.

where ρ=0.8, σ Y =3.5, σ X =2.5

The estimated regression equation of Y corresponding to X is

where

… (44 more words) …

Question number: 150

» Statistical Methods » Measures of Location

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Appeared in Year: 2013

Essay Question▾

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For the following frequency distribution on 229 values:

Class

Frequency

0 - 10

12

10 - 20

30

20 - 30

x

30 - 40

65

40 - 50

y

50 - 60

25

60 - 70

18

the median is found to be 46. Find the values of x and y.

Explanation

The cumulative frequency is

Class

Frequency

Cumulative frequency

0 - 10

12

12

10 - 20

30

42

20 - 30

x

42 + x

30 - 40

65

107 + x

40 - 50

y

107 + x+y

50 - 60

25

132 + x+y

60 - 70

18

150 + x+y

Median is 46 which lies in the class 40 - 50. So, median class is 40 - 50.

Here n = 229, l = lower limit of median class = 40

cf = cumulative frequency of the

… (156 more words) …

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