Download OU B.Sc 2018 Dec 1st Year 3007 Statistics Descriptive Stats and Probability Question Paper

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Code No. 3007

FACULTY OF SCIENCE

B.Sc. I-Semester (CBCS) Examination, November / December 2018

Subject : Statistics

Paper - I : Descriptive Statistics and Probability

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Time : 3 Hours

Max. Marks: 80

PART - A (5 x 4 = 20 Marks)

(Short Answer Type)

Note : Answer any FIVE of the following questions.

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1. Define Arithmetic mean, Geometric mean and Harmonic mean.
2. Define Central and Non-central moments. State their interrelation.
3. Define (i) Independence of events (ii) Pairwise independence and (iii) mutual independence of events.
4. Prove that for any three events A, B and C
   P(A?B?C) = P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) + P(AnBnC)

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5. Define distribution function and state its properties.
6. The random variable X has an exponential distribution, f(x) = e^-x, x>0. Find the density function of the random variable Y = 3X+5
7. Define Mathematical expectation of a variable. Find the expectation of the number on a die when thrown.
8. What is the effect of change of origin and scale on moment generating function?

PART - B (4 x 15 = 60 Marks)

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(Essay Answer Type)

Note: Answer ALL questions.

1. (a) Define Primary data. What are the different methods of collecting and editing of primary data? Describe any one method in detail with example.

   OR

   (b) (i) Explain the concept of skewness. Obtain the limits for Karl Pearson's coefficient of skewness.
   (ii) The first four moments of a distribution about the value 4 are 1, 4, 10 and 45 respectively. Compute coefficient of skewness, Kurtosis and comment upon the results.

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2. (a) (i) Define Axiomatic approach to probability.
   (ii) Prove that for any two events A and B
   P(A|B) = P(A) - P(AnB)
   (iii) The chances of solving a problem of three persons X, Y and Z are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?

   OR

   (b) State and prove multiplication theorem of Probability for ‘n’ events.

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