ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 13 - 18 of 165
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Question number: 13
» Statistical Methods » Dispersion and Skewness
Appeared in Year: 2010
Describe in Detail
The first three moments of a distribution about the value 1 are 2, 25 and 80. Find its mean standard deviation and the moment-measure of skewness.
Explanation
Given that a = 1,
The mean is
The standard deviation is
Measure of skewness
Question number: 14
» Probability » Standard Probability Distributions » Geometric
Appeared in Year: 2013
Describe in Detail
Prove that for among the discrete distributions, the geometric distribution has the lack of memory property.
Explanation
The property of memory less is that these distributions of “time from now to the next period” are exactly the same. The property is most easily explained in terms of “waiting times.
Suppose X is a discrete random variable whose values is a non-negative. In probability theory, a distribution is… (99 more words) …
Question number: 15
» Statistical Methods » Non-Parametric Test » Sign
Appeared in Year: 2010
Describe in Detail
Describe clearly sign test. State its asymptotic relative efficiency with respect to t-test.
Explanation
Let x (1), x (2), …, x (n) be the ordered sample values from a population F (X) and M be its median.
Here we test where M 0 is the given value of the median and hence
To perform the sign test, first find the differences (X… (83 more words) …
Question number: 16
» Probability » Standard Probability Distributions » Normal
Appeared in Year: 2011
Describe in Detail
Prove that the sum of two independent chi-squared random variables is also chi-squared.
Explanation
Let X and Y are two independent chi-squared random variables with degree of freedom n and m respectively. We proof this by moment generating function. The moment generating function of chi-squared distribution is
Then moment generating function of sum of two random variable (X + Y) is
because… (64 more words) …
Question number: 17
» Statistical Methods » Correlation Ratio
Appeared in Year: 2012
Describe in Detail
Two persons Amal and Bimal come to the club at random points of time between 6 p. m. and 7 p. m. , and each stays for 10 minutes. What is the chance that they will meet?
Explanation
Let x denote the time Amal arrives at the bar and y denote the time Bimal arrives at the bar from 6 p. m. We will draw the lines y = x – 10 and y = x + 10 and shade the area in between these two lines to… (93 more words) …
Question number: 18
» Statistical Methods » Non-Parametric Test » Mann-Whitney
Appeared in Year: 2009
Describe in Detail
wo drugs were given to two batches of 6 students. The numbers of days to get a complete cure are given below:
| Durg A | 6 | 7 | 8 | 9 | 12 | 16 |
| Durg B | 10 | 11 | 13 | 14 | 15 | 17 |
Using Mann-Whitney test decide whether the median days for cure by the two drugs are equal. (Table values of U - Statistic at 0.05 level are: U 5, 5 = 2, U 5, 6 = 3, and U 6, 6 = 5. )
Explanation
Let the Durg A consider the population X and Durg B consider the population Y. The hypothesis whether two sample comes from same identical population. We test the following null and alternative hypothesis is
In Mann-Whitney test, first consider the combined ordered sequence of the sample values is
Sample:… (132 more words) …