Download SGBAU BSc 2019 Summer 2nd Sem Statistics Question Paper

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B.Sc. (Part—I) Semester—II Examination

STATISTICS

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Time : Three Hours] [Maximum Marks : 80

Note :— All questions are compulsory.

1. (A) Fill in the blanks :
   1. Karl Pearson’s coefficient of correlation is also called as ~ correlation coefficient.
   2. The point of intersection of two lines of regression is __________.
   3. Mean, mode and median of the normal distribution are __________.

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   4. In Poisson distribution mean and variance are __________.
   (B) Choose the correct alternative :
   1. For perfect negative correlation r = __________.
      1. +1
      2. -1
      3. 0
      4. =

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   2. The term regression was first studied by :
      1. Karl Pearson
      2. Bernoulli
      3. Sir Francis Galton
      4. R.A. Fisher

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   3. The __________ distribution is said to have a property of lack of memory.
      1. Binomial
      2. Poisson
      3. Exponential
      4. Negative binomial

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   4. For normal distribution f₄ = __________.
      1. 3
      2. -3
      3. 0
      4. 1 2

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   (C) Answer the following questions in one sentence each :
   1. What do you mean by dichotomous classification ?
   2. What is a correlation coefficient ?
   3. State the continuous distribution for which mean is equal to variance.
   4. What do you mean by standard normal variate ?

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2. (A) Show that coefficient of correlation lies between -1 and +1. 4 (B) Derive the formula for Spearman’s rank correlation coefficient. 4 (C) Define intraclass correlation with example. 4

   OR

   (P) Describe the Scatter diagram. 4 (Q) Show that Karl Pearson’s coefficient of correlation is independent of change of origin and scale. 4 (R) Define and state the formula for Kendall’s rank correlation. 4
3. (B) Obtain the normal equations for fitting a straight line. 4 (C) Explain the term multiple correlation with the help of example. 4

   OR

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4. (P) Define the two regression coefficients. Prove any one property of regression coefficient. 4 (Q) Derive the equation of line of regression of Y on X 4 (R) Obtain the normal equations for fitting an exponential curve. 4
5. (A) Explain the term consistency of data. Obtain the condition of consistency in case of two attributes A and B. 4 (B) Explain independence of attributes. State the criteria for independence of the attributes A and B. 4 (C) Examine the consistency of given data N = 1000, (A) = 600, (B) = 500, (AB) = 50. 4

   OR

6. (P) Define the following terms :
   1. Ultimate classes
   2. Association of attributes

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   3. Order of classes and class frequencies
   4. Positive class and negative class
   4 (Q) Give the criteria for consistency of two attributes A, B and C. 4 (R) Derive the relationship between Yule's coefficient of association (Q) and coefficient of colligation s 4
7. (A) State the probability mass function of Binomial distribution and obtain its cumulant generating function. 6 (B) Obtain mean and variance of discrete uniform distribution. 6

   OR

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8. (P) Derive the recurrence relation for the moments of Binomial distribution. 6 (Q) Obtain the mgf of negative binomial distribution and hence find its mean and variance. 6
9. (A) Obtain the moment generating function of Poisson distribution. 4 (B) Obtain mean and variance of hypergeometrice distribution. 4 (C) Define geometric distribution. Obtain its mgf and hence find mean and variance. 4

   OR

10. (Q) Show that mean and variance of the geometric distribution px(X)=qp x=0,1,2, ... are respectively qp ', qp~. 4 (R) Define Hypergeometric distribution and show that it tends to Binomial distribution under certain condition. 4
11. (A) State the pdf of continuous uniform distribution and obtain its mgf. 6 (B) State the pdf of normal distribution and obtain its mode. 6

    OR

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12. (P) State the pdf of univariate gamma distribution and obtain its mean and variance. 6 (Q) State any four chief characteristics of normal distribution. 6

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