SECTION – A
1. What do you understand by a continuous frequency distribution ? Explain various terms that are frequently used in a frequency
distribution. Also highlight the difference in inclusive and exclusive methods of classes.
2. Consider the following matrix of transition probabilities of a product available in the market in two brands.
| Brand A | Brand B | |
| Brand A | 0.9 | o.1 |
| Brand B | 0.3 | 0.7 |
Determine the market shares of each of the brand in equillibrium position.
3. A manufacturer buys parts from four different vendors numbered 1, 2, 3, and 4. Referring to orders placed on two successive days, (1, 4) denotes the event that on the first day, the order was given to vendor 1 and on the second day it was given to vendor 4. Letting A represent the event that vendor 1 gets at least one of these two orders, B the event that the same vendor gets both
orders and C the event that vendors 1 & 3 do not get either order. List the elements of (a) Entire sample space (b) BUC (c) A
4. In a random sample of 500 people of a city, it was found that 160 people have a car from Maruti Suzuki family. Find a 95% confidence interval for the actual proportion of people who have a car from Maruti Suzuki family.
5. Quotations of index numbers of equity shares price of a certain joint stock company and of prices of preference shares are given below :
| Year | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 |
| Equity shares | 97.5 | 99.4 | 98.6 | 92.2 | 95.1 | 98.4 | 97.1 |
| Preference shares | 75.1 | 75.9 | 77.1 | 78.2 | 79.0 | 74.8 | 76.2 |
Use the method of Rank correlation to determine the relationship between equity share and preference share prices.
6. Write short notes on any three of the following :
(a) Inductive statistics
(b) Skewness
(c) Criterion of pessimism
(d) Double sampling
(e) Auto – correlation & Time series
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