Total No. of Questions [Total No. of Pages 03
M.C.A. DEGREE EXAMINATION, MAY 2018
Second Year
PROBABILITY STATISTICS
Time 3 Hours Maximum Marks 70
SECTION A × 15 45)
Answer any THREE questions
Q1) From vessel containing 3 white and 5 black balls, 4 balls are transferred into an
empty vessel. From this vessel a ball is drawn and is found to be white. What is
the probability that out of four balls transferred 3 are white and 1 is black?
Prove that for any three events
B and C.
Q2) A random variable has the c.d.f /500
0 0

1 0 x
x
x
e x −


−

Find the 200) and
Q3) X is normally distributed and the mean of X is 12 and standard deviation is 4. Find out
the probability of the following
20 .
20 .
0≤X≤12.
Find x1, when 0.24 .
Q4) Fit a curve of the form y aebx from the following data:
1 2 3 4 5 6
1.6 4.5 13.8 40.2 125 300
Q5) Find the value of Chi-square for the following data
Observed frequency 10 4 15 18 20 15 5 2 3
Expected frequency 10 7 10 15 25 10 5 5 5
SECTION B × 4 20)
Answer any FIVE questions
Q6) If A and B are two mutually exclusive events, show that
P A|B


−
.
Q7) Define marginal and conditional probabilities of a bivariate probability
distribution.
Q8) X and Y are independent random variables with variance 2 and 3. Find the variance of
3X 4Y.
Q9) A continuous random variable X has a.d.f. f x≤1. Find such that
p p .
Q10) Describe the F-test for testing equality of variances.
Q11) Obtain the correlation co-efficient to the following data
x10 14 18 26 30
y 18 12 24 30 36
Q12) Explain the method of least squares. Fit a straight line y a bx to the data given
below by the method of least segment.
X 5 10 15 20 25
Y 16 19 23 26 30
Q13) Write short notes on statistical quality improvement programs.
SECTION C × 1
Answer ALL questions
Q14) State the Bayesian Rule.
Q15) Define continuous random variable.
Q16) Define statistical hypothesis.
Q17) Define correlation co-efficient.
Q18) What is normal distribution?