Total No. of Pages : 02
Total No. of Questions : 18
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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
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INSTRUCTIONS TO CANDIDATES :
- SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
- SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.
- SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.
SECTION-A
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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.
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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 it are 1/2, 1/3 and 1/4 respectively. Find the probability that problem will be solved, if all of 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?
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Q10 Find the mean and variance of the density function f(x) = ae-ax, a > 0.
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.
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Q13 Two random samples are drawn from two normal populations are as follows :
Sample A: 17 27 18 25 27 29 13 17
Sample B: 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.
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Q15 Find the value of correlation coefficient between x and y using the following result obtained after performing 15 experiments.
Sx=1004, Sx2=750, Sxy=2055 Sy=280, Sy2=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=35.
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.
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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 = ax2 fits the following data :
x: 0.5 1 1.5 2 2.5
y: 0.5 2 4.5 8 12.5
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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 download link is referred from the post: PTU B.Tech Question Papers 2020 December (All Branches)