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[QUOTE=hemalathaijt;196214][B]Bangalore University
Government Science College
B.Sc. Statistics Model Question Paper
First Semester: Theory Paper
STP1: Basic Statistics and Probability
Duration: 3 Hrs.                                         Max Marks: 60[/B]

Instructions: 1.Answer Section A, Section B and any four question from Section C
2. Answer sub-divisions from Section A in the first two pages only.
                     
[B]Model Question List [/B]: [URL]http://gscblr.kar.nic.in/Exam_Papers.html[/URL]
[B]Model Question Paper[/B] : [URL]http://gscblr.kar.nic.in/files/Statistics.doc[/URL]

SECTION ‘A’
Answer any Six Sub-division: (2 Marks each)
1.a. Distinguish between (i) Nomial and ordinal data (ii) Simple and weighted averages
b. State the propertics of arithmet- Mean
c. What is curve Fitting?
d. If two regression lines are 3x+xy-26=0 and 6x+y-31=0 find correlation coefficient.
e. Prove the Laspeyrc’s price index number is the weighted A.M. of the price relatives.
f. What is time series? State the models used in time series analysis.
g. Define conditional probability.
h.Given P (A)=0.3 P(A UB)=0.6 P(B)=p find p if (i) A & B are mutually exclusive (ii)A &B are independent.

SECTION ‘B’
Answer any three Sub-division: (4 Marks each)
2.a. What are partition values? How are they determined graphically? Explain
b. What is skew ness? Describe its various measures.
c. What is scatter diagram? Interpret various types of correlation coefficient using scatter diagram.
d.Explain the various steps involved in the construction of consumer price index numbers 
e. Define “sample space” and “event”. Write the sample space of the random experiment of throwing two dice.

SECTION ‘C’
Answer any four Sub-division: (9 Marks each)
3.a) Define weighted Arithmetic mean, Find the weighted arithmetic mean of first ‘n’ natural numbers, with weights being corresponding numbers.
b) Derive the formula for mode in case of a continuous frequency distribution          (4+5)

4.a) Define mean deviation and prove that is  least when it is measured from the median
b) Define Kurtosis and prove that moment co-efficient of Kurtosis is independent of change of origin and scale.                                                                                            (5+4)

5.a) Describe the principle of least squares in curve fitting. Obtain the normal equations-for fitting curve of the type y=a+bx
b) Derive the expression for spearman’s Rank correlation co -efficient.                     (4+5)

6.a) Explain the method of obtaining seasonal indices by the method of ratio to moving average.                                                                                                             
b) Explain time and factor reversal tests and show that Fisher’s index number satisfies both the tests.                                                                                                                (4+5)

7.a) Define mutually exclusive events. Two cards are drawn from a pack of playing cards randomly. Find the probability of getting i) Two kings, (ii) One spade and one clcb. iii) An ace and a knave.
b) If A and B are two events then prove that i) P (AUB)= P (A)+P (B)-P (AUB)      (4+5)

8. a) Whate are independent events? Obtain the total number of conditions required for mutual independence of ‘n’ events.                                                                                   (4+5)
b) State Bayes theorem.                                                                                                 (4+5)
Three urns contain 2 white and 3 black balls. 3 White & 2 black balls and 4 white and I black ball respectively. One ball is drawn from an urn chosen at random and it was found to be white. Find the probability that it was drawn from the first urn.[/QUOTE]

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