Download SGBAU BSc 2019 Summer 1st Sem Statistics Question Paper

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B.Sc. (Part-I) Semester-I Examination

1S : STATISTICS

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Time : Three Hours] [Maximum Marks : 80

Note :— All questions are compulsory.

1. (A) Fill in the blanks :
   1. Deciles divide the series into __ equal parts.
   2. Probability lies between __ and __.
   3. The mathematical expectation of product of random variables is the product of their expectation.

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   4. The most stable measure of dispersion is __.
   (B) Choose the correct alternative (MCQ) :
   1. The ideal measure of central tendency is :
      1. Arithmetic mean
      2. Harmonic mean
      3. Geometric mean
      4. Mode

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   2. The highest level of scale of measurement is :
      1. Ordinal scale
      2. Nominal scale
      3. Ratio scale
      4. Interval scale

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   3. If P(A) = 0 then event A is called :
      1. Probable event
      2. Sure event
      3. Impossible event
      4. None of these

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   4. Standard deviation depends upon :
      1. Origin
      2. Scale
      3. Origin and Scale
      4. None of these

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   (C) Answer in one sentence each :
   1. What do you mean by nominal data ?
   2. Define random variable.
   3. What is median ?
   4. Define raw moment.

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2. (A) Explain primary data and secondary data. (B) Explain the function of NSSO. (C) Define :
   1. Ratio scale
   2. Interval scale.
   OR
3. (P) What are the importance of statistics ? (Q) What are the functions of CSO ? (R) What are the limitations of statistics ?

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4. (A) Show that algebraic sum of deviations of various values taken from arithmetic mean is zero. (B) How will you obtain median in case of continuous frequency distribution ? (C) Explain classification of data. State its various types. OR
5. (P) Define arithmetic mean. State its merits and demerits. (Q) Define the term less than and more than cumulative frequency distribution. (R) Obtain the relation between standard deviation & root mean square deviation.
6. (A) State the characteristics of an ideal measure of dispersion. (B) Obtain the relationship between central moments and raw moment. OR
7. (P) Show that standard deviation is least value of root mean square deviation. (Q) Define Range and Coefficient of Range. (R) Show that variance is independent of change of origin but not of scale.
8. (A) State axioms of probability. (B) Define :
   1. Favourable Event

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   2. Random Experiment.
   (C) A card is drawn from a well shuffled pack of playing cards. What is the probability that it is either a spade or an ace ? OR
9. (P) What is the chance that non-leap year selected at random will contain 53 Sundays ? (Q) Prove that : P(A?B) = P(A) + P(B) - P(AnB) where A and B are any two events.
10. (A) Define axiomatic approach of the probability. (B) Define distribution function of a random variable X and prove that : P(a < X < b) = F(b) - F(a)
11. (P) Define variance of random variable in terms of mathematical expectations. Show that ; V(ax + b) = a²V(x) OR

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12. (Q) If F is distribution of r. v. x then. F(-8) = lim F(x) = 0 F(8) = lim F (x) = 1
13. (A) Prove that :
    1. E(ax+b)=aE(x)+b
    2. E (ax) = a E(x)
    3. V (ax + b) = a²V(x)

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14. (B) Let X be the r.v. with p.d.f.
    X : 0 1 2 3
    P(x): 1/3 1/2 1/24 1/8
    Find E(x), E(x’) and V(x)
15. (P) Define moment generating function. Find its effect of change of origin and scale. OR

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16. (Q) State and prove addition property of m.g.f. Prove that M'_x (t) = M_x(ct)
17. (A) Explain joint probability mean function of marginal and conditional probability functions.

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