Sem- II , Model Paper -II

SECTION - A

Answer any Five questions:                                                                 (5*4=20M)      

1. Define Binomial distribution. Obtain mean and variance.

2. Derive mode of Poisson distribution.

3. Derive m.g.f of Poisson distribution. Hence find mean and variance.

4. Define Exponential distribution. Obtain mean and variance.

5. Obtain median of the Normal Distribution.

6. State Central limit theorem

7. Define Beta Distribution of 1^st and 2^nd kind.

8. State and prove Additive property of Geometric distribution.

SECTION - B

Answer all four questions:                                                                   (4*15=60M)

9.(a).Define Poisson distribution. Derive Recurrence relation for moments of Poisson    
       distribution.       

                                                            (OR)

   (b). Prove that Poisson distribution is the limiting of Binomial distribution by
           stating the conditions.

10. (a) .I. Obtain m.g.f of Geometric Distribution. Find mean and variance of
                geometric distribution.

            II. State and lack of memory property of Geometric distribution.

                                                            (OR)

      (b). Define Hyper Geometric Distribution. Obtain mean and variance.

11.(a). Define Standard normal distribution. Derive normal distribution is the limiting case of binomial distribution.

                                                            (OR)

     (b). I. Define Rectangular distribution. Obtain mean and variance.

        II. Prove that _2n = (1.3.5. ........ (2n-1))²ⁿ

12.(a).I.  State and prove Additive property of Exponential Distribution.

            II. Define Standard Cauchy distribution and write its properties

                                                            (OR)

     (b). Define Gamma Distribution. Derive Normal Disribution is the limiting case of
           Gamma Distribution.