Hall Ticket No Course Code AHS004
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
Four Year B.Tech IV Semester CIE II, APRIL 2018
Regulations: IARE-R16
COMPLEX ANALYSIS AND PROBABILITY DISTRIBUTION
(Common to AE EEE)
Time: 2 Hours Max Marks: 25
Answer all question from Part A
Answer any four questions from Part B
All parts of the question must be answered in one place only
PART A
1. Discover the points at which w coshz is not conformal.
Remember CO: 2 Marks:
List the important properties of probability mass function.
Understand CO: 2 Marks:
Define the term probability density function of a probability distribution.
Remember CO: 7 Marks:
Determine the Binomial distribution for which the mean is 4 and variance 3 Remember
CO: 9 Marks:
Draft the applications of Normal distribution. Understand CO: 11 Marks:
PART B
2. Calculate the value of
H
c
coth z
dz where c is 2. Understand CO: 4 Marks:
Determine the Bilinear transformation that maps the points in the z-plane into the
points in the w-plane. Understand CO: 4 Marks:
3. A continuous random variable has the probability density function



for x 0
otherwise
Determine Understand CO: 1 Marks:
i. k
ii. Mean
iii. Variance
Out of 24 mangoes, 6 mangoes are rotten. If we draw two mangoes, then obtain probability
distribution of number of rotten mangoes that can be drawn.
Remember CO: 1 Marks:
Page 1 of 2
4. Let X denotes the minimum of the two numbers that appear when a pair of fair dice is thrown
once. Find Understand CO: 8 |Marks:
i)Discrete probability distribution
ii) Expectation
iii) Variance
The probability density function of a random variable X is f K
x 1. Find K
and the distribution function Understand CO: 8 |Marks:
5. Average number of accidents on any day on a national highway is 1.8. Determine the probability
that the number of accidents is Understand CO: 8 Marks:
i. At least one
ii. At most one
Show that the mean, mode and median are equal in Poisson distribution.
Understand CO: 8 |Marks:
6. In a Normal distribution, of the item are under 35 and 89% are under 63. Compute the mean
and standard deviation of the distribution Understand CO: 11 Marks:
The marks obtained in statistics in a certain examination found to be normally distributed. If
15% of the students greater than or equal to 60 marks 40% less than 30 marks. Find the mean
and standard deviation. Understand CO: 13 Marks: