Veer Narmad South Gujarat University 2011-3rd Year B.Com SB-0519 Statistics : ( - 4 ) . - Question Paper

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ENGLISH VERSION

(2)    Figures to the right indicate full marks of the questions.

(3)    Simple calculator can be used.

1    Answer the following questions in short :    10

(1)    Define most efficient estimator.

(2)    Derive the relation between difference operator a and E-

(3)    Standard deviation of a normal population is 2.6.

A sample of 900 units has been drawn from it and its mean is 3.4 then find the 99% confidence limits for the normal population mean.

(4)    Explain the term 'Critical Path' in PERT.

(5)    A company consumes yearly 16,000 units. The ordering cost is Rs. 15 and price per unit is Rs. 20, inventory holding cost is 15% then find the value of EOQ.

2    (a) What is an inventory system? Explain the various    6

costs that are involved in inventory problems with suitable illustrations.

(b) A stockist has to supply 400 units of a product every 6 Monday to his customers. He gets the product at Rs. 50 per unit. The cost of ordering and transportation from the manufacturer is Rs. 75 per order. The cost of earring is 7.5% per year of cost of product Find :

(1)    The economic lot size

(2)    The total optimal cost

OR

2 What is Economic Order Quantity EOQ? Explain with    12

basic ideas involved in two different types of inventory models.

3 (a) Explain the following time estimator :    4

(1)    Optimistic time

(2)    Most likely time

(3)    Pessimistic time

OR

(3) State the advantages of PERT chart (b) Using network analysis methods :

(i)    forward pass

(ii)    backward pass

find E and L at each points for following information and draw a network diagram :

Answer the following questions :

(1)    Calculate EST, LST, EFT and LFT for each activity in the project.

(2)    Obtain the critical path for the project

(3)    Estimate the maximum duration in completing the project.

4 (a) What is meant by business forcasting ? State    6

various uses of business forecasting.

(b) Using Binomial expansion method find the figure of 6 sales in Karnataka for year 2011 from the data given below :

OR

5

4 (a) Obtain Newton Gregory's advanced differance    6

interpolation formula for equal intervals.

(b) The following are the amounts of incometax paid by 6 600 lecturers in year 2000. Find out the number of lecturers who have paid more than Rs. 12,000 but not more that Rs. 25,000 as incometax.

5 Answer any two from the following questions.    12

(1)    From the following values of the function u_x, compute the

values a²w0 ^an(l &^5uo

Uq =3 Uy = 12 llj ⁼ 81 = 200 w₄=100 w₅=8

(2)    What are the divided differences? In usual notations if

/(1) = 2, /(1,3) = 13, /(l, 3,6) = 10 and /(1,3,6,9) = 1 then

calculate the value of /(3).

(3)    Derive the Newton's divided differences formula for interpolation.

(4)    If u_x = x³ , then show that

3

bed

A random sample is drawn from normal variali

show that sample mean x is best estimator for population mean 11.

OR

6 (a) Define maximum likelyhood estimator and state its properties.

(b)    A sample of size n is taken from the exponetial population with given probability density function

/(x, 0) = 0e^_6x : 0 < x < 

0>O

then obtain maximum likelyhood function MLE for the parameter0. Also find the value of MLE; if 7

observations of sample are {5,6,15,7,6,10 and 13}.

(c)    A random sample in drawn from a poission population with parameter %. Then show that the sample mean x is an unbiased and consistent estimator of parameter %.

SB-0519]    7    [ 400 ]

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