Kurukshetra University 2008 B.A Probility - Question Paper
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34BAK/AOX PROBABILITY (Theory)
Paper : Statistics-!
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34[B.A. : 30
Time : Three Hours) (Maximum Marks : L
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34IB.bc.: 45
Note : Attempt five questions in all. selecting one question from each unit. All questions cany equal marks.
UNIT-1
1. (a) Define the following : *
(i) Classical definition of Probability.
(ii) Mutually exclusive events.
(iii) Conditional probability.
<b) State and prove Multiplication law of probability.
2. (a) State and prove Bayc's theorem.
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34(b) When arc two events said to be independent ?
If A and B are two independent events, show that a and R are also independent.
UNIT-II
3. Define a Discrete random variable and Probability mass rTvC'i'>n. For what value of K is the following function a proper probability mass function ?
X=x : -2 -1 0 1 2 3 P(X * *) ; 0.1 K 0.2 2K 0.3 K Also calculatc E(X) and V(X).
4. (a) State and prove Addition theorem of expectation.
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34(b) What is meant by Skewness and Kurtosis ? Prove
that |S521.
IP.T.O.
34/600/KD/60
UNlT-lll
5. (a) Define Binomial distribution. Discuss its additive
property.
(b) Determine the binomial distribution for which mean is 4 and variance is 4/3. Also find P(X I).
6. <a> Define Poisson distribution. What are its applications ?
Find moment generating function of a Poisson variate. (b) Define Negative binomial distribution. Prove that recurrence formula for probabilities of this distribution is
fix + I; r, P)=(**7~'/(* r, p).
(x + l)
UNIT-IV
7. (a) Define Normal distribution. Stale its important
properties.
(b) Obtain the points of inflexion for the normal distribution.
8. (a) Define Exponential distribution. Show that exponential
distribution tacks memory.
(b) Show that for the uniform distribution
/(*) = : -o<jr<a 2 a
moment generating function about origin is 1
smh at. at
UNIT-V
9. State and prove Chebychev's inequality.
10. (a) Stale Central limit theorem. Discuss its role in statistics, (b) State Weak law of large numbers.
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