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B.Sc Statistics (Mathematical Expectation and Probability Distribution) Question Paper – April 2017

Code: 2306
B.Sc Second Semester Examinations March/April 2017
PART- ll: Statistics
Paper -II: Mathematical Expectation and Probability Distribution
Time: 3 Hrs                                                                                                               Max. Marks: 75
Answer any five questions. Each question carry Five marks
1. Define Mathematical Expectation ofa random variable. What is the effect of change of origin and scale on Mathematical Expectation?
2. Define moment generating function of r. v. What is the limitation of m.g.f
3. Derive mean and variance of Binomial distribution through m.g.f.
4. A hospital switchboard receives an average of 4 emergency calls in a 10 minute interval. What is the Probability that
(i) There are almost 2 emergency calls
(ii) There are exactly 3 emergency calls in a 10 minute interval.
5. Define Geometric distribution. Obtain m.g.f of geometric distribution.
6. Deline Rectangular distribution. Find its mean and variance.
7. Define Normal distribution. Explain its importance
8. Define Cauchy distribution. Explain additive property of Cauchy distribution.
Answer all questions. Each question carries 10 Marks.                                   5X10 = 50 M
9. State and prove Chebyschev’s in equality
10. (i) state and prove additive theorem on mathematical Expectation.
(ii) State and prove multiplicative theorem on mathematical Expectation.
11.  Obtain the recurrence relation for the moments in Binominal distribution.
12. Derive Poisson distribution as a limiting case of Binominal distribution under certain conditions.
13. Show that poison distribution as a limiting case of Negative binominal distribution.
14. State and prove lack of memory property of Geometric distribution.
15. Define the Gamma distribution. Show that sum of ‘k’ independent gamma verities is also a gamma
16. Define Exponential distribution. Derive its m.g.f Also find mean and variance of exponential distribution from m.g.f
17. obtain m.g.f of Normal distribution
18. obtain that sum of ‘n’ independent normal varieties its also a normal vitiate

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