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
Appeared in Year: 2009
Describe in Detail
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
Appeared in Year: 2015
Describe in Detail
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
Appeared in Year: 2010
Describe in Detail
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
Appeared in Year: 2013
Describe in Detail
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
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