B.A-B.A English PROBABILITY AND DISTRIBUTIONS(Acharya Nagarjuna University (ANU), Guntur, Andhra Pradesh-2011)

B.A./B.Sc. DEGREE EXAMINATION,
DECEMBER 2011.
(Examination at the end of First Year)
Part II — Statistics
Paper I — PROBABILITY AND DISTRIBUTIONS
Time : Three hours Maximum : 100 marks
SECTION A — (4 × 20 = 80 marks)
Answer any FOUR questions.
1. (a) How will you calculate median in case of
ungrouped data?
(b) Find the medians of the following two series.
(i) 38 34 39 35 32 31 37 30 41.
(ii) 30 31 36 33 29 28 35 36.
2. (a) Explain the concept of probability following :
(i) Mathematical or ‘a priori’ approach.
(ii) Relative frequency or empirical
approach.
(b) (i) Define random experiment, trail and
event.
(ii) What do you understand by
(1) equally likely
(2) mutually exclusive and
(3) independent events.(DBSTT 11/
3. (a) Define a random variable and its
mathematical expection.
(b) A random variable X has the following
probability function.
x: –1 0 1 2
p(x) : 1/3 1/6 1/6 1/3
Compute the expection of x.
4. (a) Discuss different types of variables with
examples.
(b) What is the probability mass function
(p.m.f)?
5. (a) What do you understand by binomial
distribution? What are its main features?
(b) 12% of the items produced by a machine are
defective. What is the probability that out a
random sample of 20 items produced by the
machine, 5 are defective?
6. (a) Name the six situations where Poisson
distribution can have applications.
(b) The average number of customers, who
appear at a co center of a certain bank per
minute is two. Find the probability that
during a given minute.
(i) No customer appears
(ii) Three or more customers appear.(DBSTT 11/
7. (a) Define normal distribution. What are the
main characteristics of a normal
distribution?
(b) X ~ N (0.1). Find out which one is greater
p(- 0.5£ x £ 0.1) or p(1 £ x £ 2).
8. (a) State the conditions under which a binomial
distribution tends to
(i) Poisson distribution
(ii) Normal distribution
(b) A random variable X is normally distributed
with mean m = 12 and s.ds = 2. Find
p(9.6 < x < 13.8).
SECTION B — (10 × 2 = 20 marks)
Answer ALL questions.
9. Explain very briefly the following :
(a) Sheppard’s corrections.
(b) Skewness.
(c) Quartiles.
(d) Distribution function.
(e) Probability mass function.
(f) Central limit theorem.
(g) Geometric distribution.
(h) Negative Binomial distribution.
(i) Characteristic function
(j) Rectangular distribution

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