Download JNTUH (Jawaharlal nehru technological university) MCA (Master of Computer Applications) 1st Sem (First Semester) Regulation-R17 2018 June-July 841AD Probability And Statistics Previous Question Paper
R17
Code No: 841AD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MCA I Semester Examinations, June/July - 2018
PROBABILITY AND STATISTICS
Time: 3hrs
Max.Marks:75
Note: This question paper contains two parts A and B.
Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B
consists of 5 Units. Answer any one full question from each unit. Each question carries
10 marks and may have a, b, c as sub questions.
PART - A
5 ? 5 Marks = 25
1.a) A bag contains 26 red balls and 24 green balls. If one ball is randomly selected
from this bag, find the probability that this ball is i) red and ii) green.
[5]
b) Define discrete and continuous random variables with an example of each.
[5]
c) If a random sample of size 81 is taken whose variance is 20.25 and mean is 32, construct
98% confidence interval.
[5]
d) Explain errors in sampling.
[5]
e) Derive normal equations to fit a straight line of the form y ax b for a given
set of N data points (x , y ), i 1, 2, ..... N
i
i
.
[5]
PART - B
5 ? 10 Marks = 50
2.a)
State and prove addition theorem of probability.
7
1
b) Let A and B be two events with P(A B) , P(A B) and
8
4
P A 5
. Find i) P( )
A ii) P(B) iii) P( A B) .
[5+5]
8
OR
3.a)
State and prove Baye's theorem.
b)
A business man goes to hotels A, B, C, 20%, 50%, 30% of the times respectively. It is
known that 5%, 4%, 8% of the rooms in A, B, C hotels have faulty plumbings. What is the
probability that the business man's room having faulty plumbing is assigned to hotel C?
[5+5]
4.a)
A random variable X has the following probability distribution.
X :
0
1
2
3
4
P(X):
C
2C
2C
C2 5C2
Find i) C and ii) the distribution function of X .
3
b)
A continuous random variable X has pdf f (x) 2
x
1 , 0 x 1. Find
4
i) ` a ' such that (
P X a) (
P X a) and ii) mean of X.
[5+5]
OR
5.
Find the mean and variance of Normal distribution.
[10]
6.
Let S 1,5,6,
8 . Find the probability distribution of the sample mean for random sample
of size 2 without replacement.
[10]
OR
7.
In how many ways estimation can be done and what are they? Explain in detail. [10]
8.
In two large populations, there are 30% and 25% respectively of fair haired people. Is this
difference likely to be hidden in samples of 1200 and 900 respectively from the two
populations?
[10]
OR
9.
Two independent samples of sizes 8 and 7 had the following values.
Sample A 11 11 13 11 15 9 12 14
Sample B 9 11 10 13 9 8 10
Is the difference between the means of samples significant?
[10]
10.
Construct the least squares linear and quadratic approximations to the following data:
[10]
x :
1
2
3
4
5
y :
2.5
4.5
3.7
5.0
4.2
OR
2
2
2
11.
Show that
x
y
x y
r
, where 2
2
2
, ,
x, y, x y
2
x
y
x are variances of
y
x
y
respectively. Hence find the correlation coefficient r for the following data:
[10]
x :
6
5
8
8
7
6
10
4
9
7
y :
8
7
7
10
5
8
10
6
8
6
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This post was last modified on 16 March 2023