Download OU (Osmania University) B.Sc (Bachelor of Science) 2016 April 1st Year 2025 Statistics Previous Question Paper
FACULTIES OF ARTS AND SCIENCE
B.A. I B.Sc. I ? Year Examination, March I April 2016
Subject : STATISTICS (Theory)
Paper ? I : Descriptive Statistics and Probability Distributions
Time : 3 hours Max. Marks : 100
Note : Answer all questions. Answer questions I to IV by choosing any two
from each and any three from question V. All questions carry equal
marks. Scientific calculators are allowed.
I 1 a) Distinguish between primary data and secondary data??j E
b) What do you understand by coefficient of variation? .ejai?ierage runs
scored by three batsman A. B and C in a series gf?ig nfhgs are 50, 48
and 12. The standard deviations of their gru?Ts ige 15, 12 and 2
respectively. Who is more consistent of the thre?i???g: ~Ethan?
2 3) Define the raw and central moments of?a fregyency distribution. What wiil
be the effect of change of origin and 5" ,ie on these.
b) Show that for a frequency distributidtgiath g oefficient of kurtosis is greater
than unity. 53ers ?
?;a $3
3 State and prove addition theorem o?me?abiiity for n events.
4 a) If A and B are mdggehg t events then show that K and Eare also
independent. E?s?
afg?t
b) If P(AUB)=?~ ?awn B)=?3? and P(?)=
B are indepe???t
a:
g?
x
it 5 Let Y b?th rendom variable with the pdf
-12-. Prove that the events A and
?? 4? ,Os $4
{643?( Y) Y
0, elsewhere
a) Find the expected value and variance of Y.
b) Let X = 300 y + 50. Find E(X) and Var(X).
6 a) Write the procedure for transformation of one-dimensionai random
variable. _ 3
b) if f(x) = 2x ; O < x < 1, find the probability density function of Y = 8x .
7 Define MGF and CGF of a random variable. What is the effect of change of
origin and scale on MGF and CGF? ?
Code No. 2025
_ 2 _ V
8 a) State and prove Chebyshev?s inequality.
b) A discrete random variable X takes the values 0, 1, 2, 3 with probabilities
??WSE?S-? respectively. Evaluate P{lx ? pl 2 20}.
iii 9 Define Binomial distribution. Obtain its MGF and hence find mean and
va?ance.
10 a) Show that Poisson distribution satisfies the reproductive property.
b) The number of monthly breakdowns of a computer is a rag??? variable
. . . ,.. b'
?4?
X havmg a Pmsson distribution With mean 2 Fmd the 531%, ?(a that this
computer wilt function for a month .. .. 6?
i) without a breakdown ii) with exactly q??ghg ,kdown.
11 Define Negative Binomial Distribution. Derive its mj?erS?
and hence show that mean < variance. ?
12 Prove that Binomial distribution is the timitm? case of Hyper Geometric
distribution by stating the conditions; 3% ,7
iv 13 The mean and variance of a coniiggg uniform random variable X are 1.5
and 0.75 respectively. ?
i) Obtain the probability density function of X.
ii) Obtain the Quartiiesv ingnile deviation.
14 Show that for a Norgna ution QD : MD : SD: : 10: 12: 15.
_ ?31.; g
15 i) Mention the @311ng ?h?iracteristics of normal distribution.
ii) Suppose that '??during transcendental meditation the reduction in
consumptign of oxygen by a person is a random variable having normal
dist?lggtio? with mean 37.6 cc per minute and standard deviation 4.6 cc.
Riga trig: probability that during meditation this reduction will be atmost
g3?" [Table values : P(O < Z < 0.56) = 0.2128].
16 Eating Beta distribution of second kind. Find its mean and variance.
V Write short note on any three of the following :
17 Difference between Questionnaire and schedule
Q&Baye?s theorem
?Cauchy ? Schwartz?s inequality ?
29* dditive property of Gamma distribution
Mack of memory property of exponential distribution
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This post was last modified on 18 April 2020