Download OU B.Sc 2016 April 1st Year 2025 Statistics Question Paper

Download OU (Osmania University) B.Sc (Bachelor of Science) 2016 April 1st Year 2025 Statistics Previous Question Paper

Code No. 2025
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