Semester - II Model paper - I


                 SECTION- A

I. Answer any Five questions:                                                                   5*4=20M

1.    Define Bernoulli distribution.  Obtain Mean and Variance.
2.    Define discrete uniform distribution. Obtain Mean and Variance.
3.    State and prove additive property of Binomial distribution.
4.    Define Geometric distribution. Derive its moment generating function .
5.    Define Cauchy distribution, write its properties.
6.    Write chief characteristics of normal distribution.
7.    The mean and variance of a continuous uniform random variable ‘x’ are 1.5 and 0.75 respectively. Obtain the probability density function of ‘x’.
8.    Sate weak law of large numbers. 

SECTION -B

 II. Answer all questions:                                                                 4*15=60M
9(a). Define negative binomial distribution. Derive its mean and variance through       expectation.                                                    (OR)
  (b). Define Hyper geometric distribution, give an example. Obtain its Mean and Variance.

10(a).(i). Define Binomial distribution. Obtain moment generating function.
          (ii). Prove that Binomial distribution is the limiting case of Hyper geometric        distribution by stating the conditions.                                   
                                                                        (OR)
    (b).(i). Show that Poisson distribution satisfies the reproductive property.
          (ii).The number of monthly breakdowns of the computer is a random variable “X”      having a  Poisson Distribution with mean 2. Find the probability that this computer          will function for a month (a).Without a breakdown  (b).With exactly one breakdown

11(a). Define Standard normal distribution. Derive normal distribution is the limiting case     of Poisson distribution.               (OR)
     (b). (i) Define exponential distribution. Obtain its moment generating function.
      (ii) State and prove its lack of memory property.

12(a). Show that for a Normal distribution, QD :  MD  :  SD  = 10  :  12  :  15  
                                                                        (OR)
(b) Define Beta distribution of 1st and 2nd kinds.  Obtain Mean and Variance of these   distributions.

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