Download JNTUH MCA 1st Sem R17 2018 June-July 841AD Probability And Statistics Question Paper

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





---oo0oo---