Download JNTUA (JNTU Anantapur) MCA (Master of Computer Applications) 2014 August Supplementary 1st Sem 06MC104 Probability And Statistics Question Paper
Code: 06MC104
MCA I Semester Supplementary Examinations August 2014
PROBABILITY & STATISTICS
(For 2008 admitted students only)
Time: 3 hours Max. Marks: 60
Answer any FIVE questions
All questions carry equal marks
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1 (a) A and B throw alternatively with a pair of dice one who first throws a total of nine wins. What are their
respective chances of winning if A starts the game?
(b) Define conditional probability. State and prove Baye?s theorem.
2 (a) (i) Define descrete distributive function.
(ii) Given that ???? ( ???? ) =
???? 2 ???? ? , is a probability distribution for a random variable X that can take on the
values x = 0, 1, 2, 3 and 4. Find k, mean and variance of x.
(b) (i) Define continuous distributive function.
(ii) The cumulative distribution function for a continuous random variable X is ???? ( ???? ) = ?
1 ? ???? ?2 ???? , ???? ? 0
0, ???? < 0
then find density function ???? ( ???? ), mean and variance.
3 (a) It has been found that 2% of the tools produced by a certain machine are defective. What is the
probability that in a shipment of 400 such tools:
(i) 3% or more
(ii) 2% or less will prove defective.
(b) List the properties of normal distribution.
4 (a) Find the mean and standard deviation of sampling distribution of variances for the population 2, 3, 4,
5 by drawing samples of size two
(i) with replacement
(ii) without replacement.
(b) What is the effect on standard error, if a sample is taken from an infinite population of sample size
increased from 400 to 900?
5 (a) Prove that for a random sample of size n, ???? 1
, ???? 2
? ? ? ? ???? ???? taken from an infinite population ???? 2
=
1
???? ? ( ???? ???? ? ???? ?)
2 ???? ???? =1
is not an unbiased estimator of the parameter ???? 2
but
1
???? ?1
? ( ???? ???? ? ???? ?)
2 ???? ???? =1
is unbiased.
(b) A random sample of size 100 is taken from a population with ???? = 5.1. Given that the sample mean is
???? ? = 21.6, construct a 95% confidence interval for the population mean ???? .
6 (a) In 64 randomly selected hours of production, the mean and the standard deviation of the number of
acceptance pieces produced by an automatic stamping machine are ???? = 1.038 and ???? = 0.146
(b) In an investigation on the machine performance the following results are obtained.
No. of units inspected No. of defectives
Machine 1 375 17
Machine 2 450 22
Test whether there is any significant performance of two machines at ???? = 0.05.
7 (a) Explain student ? distribution, its properties and applications.
(b) The mean life time of a sample of 25 fluorescent light bulbs produced by a company is computed to
be 157 hours with a S.D of 120 hours. The company claims that the average life of the bulbs
produced by the company is 1600 hours using the level of significance of 0.05. Is the claim
acceptable?
8 (a) Write characteristics of (m/m/1): ( ?/FIFO) model.
(b) What is queuing problem?
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This post was last modified on 28 July 2020