Semester-I, Model Paper-II


Model Paper - II
Subject: STATISTICS, Paper-I: Descriptive Statistics and Probability
Time: 3 hr                                                                                                        Max. Marks: 80
SECTION - A
Answer any Five questions:                                                                        5 X 4 = 20
1.What are the differences between primary and secondary data.
2.Explain Kurtosis.
3.State and prove Baye’s theorem.
4.Explain classical and statistical definition of probability and give their limitations.
5.Suppose that X is uniformly distributed over (0,2) .Find the density of Y=X2
6.Define distribution function and state its properties.   
7.Define PGF and find its mean and variance.
8.State and prove addition theorem of expectation.
SECTION - B
Answer all 4 Questions:                                                                                4 X 15 = 60
9.(a).(i).Explain secondary data. What are the sources of getting secondary data.
      (ii).Distinguish between questionnaire and schedule.
                                                            (OR)
(b).(i).Define central and non-central moments. What will be the effect of change of
           origin and scale on these moments.
                  (ii).The mean of 100 items was 50.later on it was found that two items were misread as
18    nd 6 instead of 81 and 66. Find the correct mean.
10.(a).(i).State and prove multiplication theorem of probability for n-events.
                   (ii).If E1 and E2 are independent events then show that E1 and E2 are also independent.  
(OR)
            (b). Define the following with examples
       (i).Random experiment (ii).Mutually exclusive events(iii).Compound event
      (iv).Equally likely events (v).Independent events
11.(a).(i).From the following find a) the probability mass function of x  
                        (ii).P(x is even), P(x is odd), P(x<2), P(1<x<8)
            X          -3       -1        0         1         2         3         5         8
F(X)     0.10    0.30     0.45     0.5       0.75     0.90     0.95     1.00
                                                (OR)
      (b). A continuous random variable X has the following probability law    
            f(x)      =Ax2    ; 0X1  
= 0       ; otherwise
     Determine   a) find the value of A    b) find mean   c) P(0.2X10.5)
12.(a).(i). Define characteristic function. state and prove its properties.
      (ii). Obtain relation between moments and cumulants.
(OR)
            (b).(i).Define mathematical expectation, mean and variance in terms of expectation.
      (ii) State and prove Chebyshev’s inequality.                           

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