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

Essay Question▾

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.


Given that a = 1,

The mean is

The standard deviation is

… (99 more words) …

Question number: 14

» Probability » Standard Probability Distributions » Geometric


Appeared in Year: 2013

Essay Question▾

Describe in Detail

Prove that for among the discrete distributions, the geometric distribution has the lack of memory property.


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 said to have lack of memory if

… (118 more words) …

Question number: 15

» Statistical Methods » Non-Parametric Test » Sign


Appeared in Year: 2010

Essay Question▾

Describe in Detail

Describe clearly sign test. State its asymptotic relative efficiency with respect to t-test.


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 diffe

… (112 more words) …

Question number: 16

» Probability » Standard Probability Distributions » Normal


Appeared in Year: 2011

Essay Question▾

Describe in Detail

Prove that the sum of two independent chi-squared random variables is also chi-squared.


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

… (95 more words) …

Question number: 17

» Statistical Methods » Correlation Ratio


Appeared in Year: 2012

Essay Question▾

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?


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 denote the event.

Finding a ration this cube

Finding a Ration this Cube

Calculate the point’s x and y

They will meet if x - 10 < y < x + 10 that is (x, y) falls in th

… (52 more words) …

Question number: 18

» Statistical Methods » Non-Parametric Test » Mann-Whitney


Appeared in Year: 2009

Essay Question▾

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







Durg B







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. )


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

… (131 more words) …