Download JNTUH (Jawaharlal nehru technological university) MCA (Master of Computer Applications) 1st Sem (First Semester) Regulation-R13 2021 July-August 811AD Probability And Statistics Previous Question Paper
R13
2021
Code No: 811AD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MCA I Semester Examinations, July/August - 2021
PROBABILITY AND STATISTICS
Time: 3 Hours
Max.Marks:60
Answer any five questions
All questions carry equal marks
- - -
1.a)
Two digits are selected at random from the digits 1 through 9.
i) If the sum is odd, what is the probability that 2 is one of the digit selected.
ii) If 2 is one of the digits selected, what is the probability that the sum is odd?
b)
A fair coin is tossed until a head or five tails occurs. Find the expected number of tosses
of the coin.
[6+6]
2.a)
State and prove Boole's inequalities
b)
A, B, C in order toss a coin. The first one to toss head wins the game. What are the
probabilities of winning, assuming that the game may continue indefinitely?
[6+6]
3.a)
A continuous random variable X has the probability density function
f x
2x,
if
0 x 1
0,
otherwise
1
3
Find the cumulative distribution function for X. Also find P
X
and
4
4
1
P X
.
2
b)
Find the probability of getting 1 or 4 or 5 or 6 in throwing a die 5 to 7 times among
9 trials using normal distribution.
[6+6]
4.
Show that for normal distribution the quartile deviation, mean deviation and standard
deviation are approximately 10:12:15.
[12]
5.a)
Determine the mean and standard deviation of the sampling distribution of means of
300 random samples each of size 36 are drawn from a population of size 1500 which is
normally distributed with mean 22.4 and standard deviation 0.048, if sampling is done
i) with replacement and ii) without replacement.
b)
Construct 95% confidence interval for the true proportion of computer literates if 47 out
of 150 persons from rural areas are computer literates.
[6+6]
6.a)
A normal population has a mean 0.1 and a standard deviation of 2.1. Find the
probability that the mean of simple sample of 900 members will be negative.
2021
b)
In a study conducted for 500 days, only on 4 days it was recorded that `lead' content in
a famous river exceeded 200mg/cm. Construct an upper 99% confidence limit for the
probability that the `lead' content in the river will exceed 200mg/cm on any one day.
[6+6]
7.a)
A briefcase manufacturing company claims that 80% of executives carried briefcases
produced by them. Verify its claims if in a random sample of 900 executives, 675 used
the company's briefcases. Use 5% level of significance.
b)
Explain, stating clearly the assumptions involved, the t-test for testing the significance
of the difference between the two sample means.
[6+6]
8.
The tangent of the angle between two regression lines is 0.6 and if x= 1y, find the
2
correlation coefficient between x and y.
[12]
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This post was last modified on 16 March 2023