M.C.A. DEGREE EXAMINATION, MAY 2017
Second Year
PROBABILITY AND STATISTICS
Time 3 Hours Maximum Marks 70
SECTION A × 15 45)
Answer any THREE questions
Q1) Prove Baye's theorem and explain with suitable example.
Q2) Companies B1, B2, B3 produce 25% of the cars respectively. It is known
that of these cars produced from B1, B2, B3 are defective.
What is the probability that a car purchased is defective.
If a car purchased is found to be defective what is the probability that this car is
produced by the company B.
Q3) Take 30 slips of paper and label 5 each-4 and four each 3 and three each 2 and
2 and each-1, 0 and if each slip of the paper has the same probability of being drown
find the probabilities of getting 4 and find the mean and
variance of this distribution of means.
Q4) The following data pertain to the number of computer jobs per day and the required
CPU time required:
No. of jobs X 1 2 3 4 5
CPU time Y 2 5 4 9 10
Fit a least square line to estimate the mean CPU time and using it estimate the CPU
time at x 3.5
Q5) Measuring specimens of nylon yarn taken from two machines, it was found that 8
specimens from 1st machine had a mean denier of 9.67 with a standard deviation of
1.81 while 10 specimens from a 2nd machine had a mean denier of 7.43 with a standard
deviation 1.48. Assuming the population are normal test the hypothesis
H0 2=1.5 against 2>1.5 at 0.05 level of significance?
SECTION B × 4 20)
Answer any FIVE questions
Q6) Explain the Probability generation functions with example.
Q7) If the mean and S.D. of normal distribution are 70 and 16, find p x 46.
Q8) Derive the formula to find the mean and variance of Binomial distribution.
Q9) Two digits are selected at random from the digits 1 through 9.
If the sum is odd, what is the probability that 2 is one of the numbers selected.
If 2 is one of the digits selected, what is the probability that the sum is odd 10.
What do you mean?
Q10) What is the probability that X will be between 75 and 78 if a random sample of size
100 taken from an infinite population has mean 76 and variance 256?
Q11) Two dice are thrown. Let X the random variable assign to each point in S the
maximum of its numbers. Find the distribution, the mean and variance of the
distribution.
Q12) Fit a curve of the form y axb by the method of least squares for the following data:
X 1 2 3 4 5
Y 5 2 4.5 8 12.5
Q13) The performance of a computer is observed over a period of 2 years to check the claim
that the probability is 0.20 that its downtime kwill exceed 5 hours in any given week.
Testing the null hypothesis P 0.20 against the alternate hypothesis P 6 0.20, what
can we conclude at the level of significance α 0.05, if there were only 11 weeks in
which the downtime of the computer exceeded 5 hours?
SECTION C × 1
Answer ALL questions
Q14) What is conditional probability.
Q15) What is the objective of Uniform exponential distribution.
Q16) Define a sampling.
Q17) What are the advantages Multiple regression?
Q18) What is Mean inter-arrival time?