ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 11 - 16 of 165
Access detailed explanations (illustrated with images and videos) to 165 questions. Access all new questions we will add tracking exam-pattern and syllabus changes. Unlimited Access for Unlimited Time! View Sample Explanation or View Features.
Rs. 550.00 or
How to register?
Question number: 11
» Statistical Methods » Dispersion and Skewness
Appeared in Year: 2012
Describe in Detail
Show, by proving all intermediate results, that for a set of n unsorted data, the measure of skewness based on mean, median and standard deviation, necessarily lies between -3 and + 3.
Explanation
The formula of measure of skewness given by Karl Pearson’s is
Also, we known the relation of mean, median and mode is
Mean-Mode = 3 (Mean-Median)
So,
Using Chebyshev’s inequality, X be a random variable with mean µ and variance
… (163 more words) …
Question number: 12
Appeared in Year: 2014
Describe in Detail
In a lottery 1000 tickets are sold and the cost of a ticket is if 10. The lottery offers a first prize of if 1,000, two second prizes of if 500 each, and three third prizes of if 100 each. A person purchases a ticket. If X denotes the amount he may get, find E (X) and V (X).
Explanation
The probability of purchases a ticket is
First prize amount is 1000
Two second prizes amount is 500 each
Three third prizes amount is 100 each
X denotes the amount he may get
Then, the expected value of X is
The variance of X is
… (91 more words) …
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
… (52 more words) …
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 said to have lack of memory if
… (299 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 (i) -M 0) for i = 1,2, …, n and consider their signs. Su
… (121 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
… (103 more words) …