Download OU B.Sc 2019 June-July 2nd Semester Statistics Question Paper

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FACULTY of SCIENCE

Code No. 3037

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B.Sc. - Semester Examination, May / June 2019

Subject - Statistics

Time : 3 Hours

Max. Marks: 80

PART - A (4 x 5 = 20 Marks)

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(Short Answer Type)

Note: Answer ALL questions.

1. Find the mean and variance of the following uniform distribution obtained by tossing a die: f(x) = 1/6, x = 1, 2, 3, 4, 5, 6
2. A random variable "X" is Normally distributed with mean µ = 12 and standard deviation s = 2. You are given (i) area between 12 and 14.4 is 0.4251 (ii) area between 0 and 2.6 is 0.4953.
3. Derive the mean of an Exponential Distribution.

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4. Find the moment generating function of Gamma Distribution.
5. State any two properties of Cauchy Distribution.

PART - B (4 x 15 = 60 Marks)

(Essay Answer Type)

Note: Answer ALL the questions.

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1. (a) Derive first three central moments of a Binomial Distribution.
   OR
   (b) Explain the Moment Generating function of a Poisson Distribution and hence calculate mean and variance from it.
2. (a) A taxi cab company has 12 Maruti Swift cars and 8 Tata Indica cars. If 5 of these cars are in workshop for repair and Swift car is likely to be in for repairs as Indica car, what is the probability that:
   (i) Out of 5 cars, x of them are Swift cars in workshop for repairs.
   

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   (ii) All the 5 are of the same make.
   (iii) Find the expected value of x i.e. E(x).
   OR
   (b) Stating the conditions, prove that Poisson Distribution as a limiting case of the Negative Binomial Distribution.

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