Download OU B.Sc 2016 April 1st Year 2025 Statistics Question Paper

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Code No. 2025

FACULTIES OF ARTS AND SCIENCE

B.A./B.Sc. I-Year Examination, March / April 2016

Subject : STATISTICS (Theory)

Paper — I : Descriptive Statistics and Probability Distributions

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Time : 3 hours Max. Marks : 100

Note : Answer all questions. Answer questions I to IV by choosing any two from each and any three from question V. All questions carry equal marks. Scientific calculators are allowed.

1. a) Distinguish between primary data and secondary data.
   b) What do you understand by coefficient of variation? The average runs scored by three batsman A, B and C in a series of 10 innings are 50, 48 and 12. The standard deviations of their runs are 15, 12 and 2 respectively. Who is more consistent of the three batsman?
2. a) Define the raw and central moments of a frequency distribution. What will be the effect of change of origin and scale on these.
   

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   b) Show that for a frequency distribution the coefficient of kurtosis is greater than unity.
3. a) State and prove addition theorem of probability for n events.
   b) If A and B are independent events then show that A and B are also independent.
4. a) If P(AUB) = 5/8, P(A n B) = 1/4 and P(B) = 1/2. Prove that the events A and B are independent.
   b) Let f(y) = 64y(1/4 - y), 0 < y < 1/4
   

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   0, elsewhere
   Find the expected value and variance of Y.
   Let X = 300y + 50. Find E(X) and Var(X).
5. a) Write the procedure for transformation of one-dimensional random variable.
   b) If f(x)=2x; 0 < x < 1, find the probability density function of Y = 8x³.

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6. Define MGF and CGF of a random variable. What is the effect of change of origin and scale on MGF and CGF?
7. a) State and prove Chebyshev’s inequality.
   b) A discrete random variable X takes the values 0, 1, 2, 3 with probabilities 1/8, 1/6, 3/8, 1/3 respectively. Evaluate P{|X — 1| = 2}.
8. Define Binomial distribution. Obtain its MGF and hence find mean and variance.
9. Define Negative Binomial Distribution. Derive its mgf and hence show that mean < variance.

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10. Prove that Binomial distribution is the limiting case of Hypergeometric distribution by stating the conditions.
11. The mean and variance of a continuous random variable X are 1.5 and 0.75 respectively.
    i) Obtain the probability density function of X.
    ii) Obtain the Quartiles and Quartile deviation.
12. Show that for a Normal distribution QD : MD : SD::10:12: 15.

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13. i) Mention the chief Characteristics of normal distribution.
    ii) Suppose that during transcendental meditation the reduction in consumption of oxygen by a person is a random variable having normal distribution with mean 37.6 cc per minute and standard deviation 4.6 cc. Find the probability that during meditation this reduction will be atmost 35.0 cc. [Table values - P(0<Z<0.56)= 0.2128].
14. Define Beta distribution of second kind. Find its mean and variance.

V Write short note on any three of the following :

1. Difference between Questionnaire and schedule

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2. Baye’s theorem
3. Cauchy - Schwartz’s inequality
4. Additive property of Gamma distribution
5. Lack of memory Property of exponential distribution

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