B.Sc Corporate Statistics Question Paper 2006

Loyola College B.Sc. Statistics Nov 2006 Applied Statistics Question Paper PDF Download

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                          LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

AB 15

FIFTH SEMESTER – NOV 2006

ST 5502 – APPLIED STATISTICS

(Also equivalent to STA 507)

 

 

Date & Time : 30-10-2006/9.00-12.00   Dept. No.                                                       Max. : 100 Marks

PART – A

Answer ALL questions.                                              (10 x 2 = 20 marks )

 

  1. Explain the two causes for seasonal variations in a time series.
  2. Describe the two models commonly used for the decomposition of a time series into its components.
  3. What are the steps involved in the construction of Chain Indices ?
  4. If L ( p ) and P ( q ) represent respectively Laspayres’ index number for prices and Paasche’s index number for quantities, then show that

L ( p ) / L ( q )  =  P ( p ) /  P ( q )

 

  1. Show that the Cost of Living Index Number obtained by Aggregate Expenditure Method and Method of Weighted Relatives is the same.
  2. Discuss a suitable method to determine the population at anytime `t’ after the census or between two censuses.
  3. Explain the Merits and Demerits of Standardized Death Rates.
  4. Describe multiple correlation with an example.
  5. Write a note on world agricultural census.
  6. Briefly explain labour statistics.

PART – B

Answer any Five questions.                                              (5  x 8  = 40 marks )

 

  1. Explain the cyclical component of a time series. What are business cycles?

 

  1. Discuss the method of three selected points for fitting modified exponential curve.
  2. A company estimates its sales for a particular year to be . 24,00,000.  The seasonal indices for sales are as follows :

—————————————————————————————

Month             Seasonal                             Month              Seasonal

Index                                                            Index

—————————————————————————————-

January                         75                                 July                        102

February                        80                                August                     104

March                            98                                September               100

April                            128                                October                    102

May                             137                                 November                 82

June                             119                                 December                  73

—————————————————————————————-

 

Using this information, calculate estimates of monthly sales of the company. ( Assume that there is no trend. )

 

  1. An enquiry into the budgets of middle class families in a city gave the following information:

 

Expenses on                   Food    Rent    Clothing    Fuel     Others

 

30%       15%       20%       10%     25%

 

Prices ( in Rs. ) in 1982                100        20         70          20           40

Prices ( in Rs. ) in 1983                   90       20         60          15           35

 

Compute the price index number using :

( i )  Weighted A.M. of price relatives,

( ii ) Weighted G.M. of price relatives.

 

  1. An enquiry into the budgets of the middle class families of a certain city revealed that on an average the percentage expenses on the different groups were Food 45, Rent 15,  Clothing 12, Fuel 8 and Miscellaneous 20. The group index numbers for the current year as compared with a fixed base period were respectively 410, 150, 343, 248 and 285. Calculate the consumer price index number for the current year. Mr. X was getting Rs.240 in the base period and Rs. 430 in the current year. State how much he ought to have received as extra allowance to maintain his former standard of living.
  2. Discuss the uses of Vital Statistics.

 

  1. Mention the assumptions used in the construction of the life tables.

 

  1. Discuss in detail about mining and quarrying statistics.

                                                    PART – C

Answer any TWO questions.                                         ( 2  x  20 = 40 marks )

 

  1. You are given the population figures of India as follows :

 

Census Year ( X )        :   1911    1921    1931    1941    1951    1961     1971

Population ( in Crores):    25.0     25.1     27.9     31.9     36. 1    43.9      54.7

 

Fit an exponential trend Y = abx   to the above data by the method of least squares and find the trend values. Estimate the population in 1981.

 

  1. ( a ) Describe in detail the problems involved in the construction of

index numbers.                                                          (14 marks)

 

 

 

( b )  On a certain date the Ministry of Labour retail price index was 204.6. Percentage increases in price over some basic period were : Rent 65 , Clothing 220,  Fuel and Light 110,  Miscellaneous 125. What was the percentage increase in the food group ? Given that the weights of the different items in the group were as follows :

 

Food  60 ,  Rent 16 ,  Clothing  12,  Fuel and Light 8 , Miscellaneous 4.

( 6 marks)

 

21 ( a ). Find the standardized death rate by Direct and Indirect

methods   for the data given below:

————————————————————————————–

Standard Population                            Population A

Age      —————————————————————————

Population              Specific                  Population       Specific

in `000               Death Rate                in `000         Death Rate

————————————————————————————–

 

0-5           8                          50                              12                  48

5-10         10                        15                             13                   14

10-15        27                        10                             15                     9

>50             5                        60                             10                   59

————————————————————————————-

( 10 marks )

 

( b ).  Explain the concepts with examples:

(  i  )  Stationary Population

(  ii )  Stable Population.                                 (10 marks )

 

  1. ( a ) Find the multiple linear regression equation of X1 on X 2  and

X 3   from the data relating to three variables given below:

 

X1   :           4          6          7         9        13         15

X2    :        15        12         8          6          4          3

X3   :     30        24       20        14       10          4   ( 10  marks )

 

( b ) Discuss any two methods of national income estimation.

( 10 marks ).

 

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Loyola College B.Sc. Statistics Nov 2006 Applied Stochastic Processes Question Paper PDF Download

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                         LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

AB 09

FIFTH SEMESTER – NOV 2006

ST 5400 – APPLIED STOCHASTIC PROCESSES

(Also equivalent to STA 400)

 

 

Date & Time : 03-11-2006/9.00-12.00     Dept. No.                                                   Max. : 100 Marks

 

 

 

SECTION A

ANSWER ALL QUESTIONS.                                                                               (10 X 2 =20)

 

  1. Give an example of discrete time –continous state stochastic process  ?
  2. Give one example each for “communicative states” and “non communicative states”
  3. Define : Markov process
  4. When do you say a stochastic process has “Stationary Independent Increments” ?
  5. Identify the closed sets corresponding to a Markov chain with transition probability matrix.
  6. What is a recurrent state ?
  7. When do you say a given state is “aperiodic” ?.
  8. What is a doubly stochastic matrix.?
  9. Name the distribution associated with waiting times in Poisson process
  10. What is a martingale ? .

 

SECTION B

Answer any FIVE questions                                                                      (5 X8 =40)

 

  1. Show that a one step transition probability matrix of a Markov chain is  a stochastic matrix.

 

  1. Write a detailed note on classification of stochastic processes

 

  1. Show that every stochastic process with independent increments is a Markov process.

 

  1. Obtain the equivalence classes corresponding to the  Transition Probability Matrix

 

.

 

  1. Consider the following Transition Probability Matrix . Using a necessary and sufficient condition for recurrence, examine the nature of all the three states.

 

  1. Form the differential equation corresponding to Poisson process

 

 

  1. Messages arrive at a telegraph office in accordance with the laws of a Poisson process with mean rate of 3 messages per hour. (a) What is the probability that no message will have arrived during the morning hours (8,12) ? (b) What is the distribution of the time at which the fist afternoon message arrives ?

 

  1. Show that, under usual notations,

 

 

SECTION C

Answer TWO questions.                                                                            (2 X 20 =40)

 

  1. (a) Let be a sequence of random variables with mean 1.Show thatis a Martingale.            (8)

(b) Consider a Markov chain with TPM . Find the equivalence classes and compute the periodicities of all the 4 states  (12)

 

  1. (a) Illustrate with an example how Basic limit theorem can be used to relate stationary distributions and mean time of first time return.                      (8)

(b) Suppose that the weather on any day depends on the weather conditions for the previous two days. To be exact, suppose that if it was sunny today and yesterday, then it will be sunny tomorrow with probability 0.8; if it was sunny today but cloudy yesterday then it will be sunny tomorrow with probability 0.6; if it was cloudy today but sunny yesterday, then it will be sunny tomorrow with probability 0.4; if it was cloudy for the last two days, then it will be sunny tomorrow with probability 0.1. Transform the above model into a Markov chain and write down the TPM. Find the stationary distribution of the Markov chain. On what fraction of days in the long run is it sunny ?  (12)

 

  1. Derive under Pure-Birth Process assuming
  2. Write short notes on any of the following :

(a) One dimensional random walk      (5)

(b) Periodic states       (5)

(c) Martingales            (5)

(d) Properties of Poisson Process        (5)

 

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