Download PTU (I.K.Gujral Punjab Technical University (IKGPTU)) B-Tech (Bachelor of Technology) (EEE)- Electrical And Electronics Engineering 2020 December 4th Sem 77610 Mathematics Iii (Probability And Statistics) Previous Question Paper
Total No. of Pages : 02
Total No. of Questions : 18
B.Tech. (Electrical & Electronics) (2018 Batch) (Sem.?4)
MATHEMATICS-III (PROBABILITY & STATISTICS)
Subject Code : BTAM-302-18
M.Code : 77610
Time : 3 Hrs. Max. Marks : 60
INST RUCT IONS T O CANDIDAT ES :
1 .
SECT ION-A is COMPULSORY cons is ting of TEN questions carrying TWO marks
each.
2 .
SECT ION-B c ontains F IVE questions c arrying FIVE marks eac h and s tud ents
have to atte mpt any FOUR q ues tions.
3 .
SECT ION-C contains THREE questions carrying T EN marks e ach and s tudents
have to atte mpt any T WO questio ns.
SECTION-A
Answer the following in short :
Q1 Define Kurtosis.
Q2 Find the expected number of heads appear, when a coin is tossed twice.
Q3 Write the mean and variance of poisson distribution.
Q4 Write the formula for 2 test.
Q5 If a random variable X follows Poisson distribution such that P(X = 1) = P(X = 2), find the
mean of distribution.
Q6 Find the probability that 6 out of 10 persons will recover from fever if the probability of
recovering from fever is independent and 0.70.
Q7 A problem of mathematics is given to three students A, B and C whose chances of solving
1 2
3
it are
, and
respectively. Find the probability that problem will be solved, if all of
2 3
4
them try independently.
Q8 The mean life time of sample of 100 fluorescent light bulbs produced by a company is
computed to be 1570 hours with a standard deviation of 120 hours. The company claims
that the average life of the bulbs produced by it is 1600 hours. Obtain 95% confidence
limits of the mean of the population.
Q9 A random sample of 900 members has a mean 3.4 cms. Can it be regarded as a sample
from a large population of mean 3.2 cms and S.D. 2.3 cms?
Q10 Find the mean and variance of the density function f(x) = ae?ax, a > 0.
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SECTION-B
Q11 If the chance that any one of the 10 telephone lines is busy at an instant is 0.2, what is the
chance that 5 of the lines are busy? What is the probability that all the lines are busy?
Q12 A sample of 20 items has mean 42 units and S.D. 5 units. Test the hypothesis that, it is a
random sample from a normal population with mean 45 units.
Q13 Two random samples are drawn from two normal populations are as follows :
Sample A :
17
27
18
25
27
29
13
17
Sample A :
16
16
20
27
26
25
21
Test whether the samples are drawn from the same normal population.
Q14 In a normal distribution, 7% of the items are under 35 and 89% are under 63. Find the
mean and standard deviation of the distribution.
Q15 Find the value of correlation coefficient between x and y using the following result
obtained after performing 15 experiments.
2
x 100.4, x 750, xy 2055,
2
y 280, y 5690.5
SECTION-C
Q16 Obtain the two lines of regression from the following pairs of observations on X and
Y: (1, 3), (2, 3), (3, 5), (4, 6), (5, 5), (6, 8), (7, 8), (12, 10). Hence predict the value of Y for
X = 3.5.
Q17 Four coins were tossed 200 times. The number of tosses showing 0, 1, 2, 3, 4 heads were
found to be as under. Fit a binomial distribution to the data. Also, find the expected
frequencies.
No. of heads :
0
1
2
3
4
No. of tosses :
15
35
90
40
20
Q18 Determine the constants a and b by the least squares method such that y = axb fits the
following data :
x :
1
2
3
4
5
y :
0.5
2
4.5
8
12.5
NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any
page of Answer Sheet will lead to UMC against the Student.
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This post was last modified on 13 February 2021