Download AKTU B-Tech 2nd Sem 2014-15 EEE101 Electrical Engineering Question Paper

Code: 20A3301

II B. Tech I Semester (R20) Regular Examinations Dec-2021/Jan-2022

PROBABILITY AND STATISTICS

(Common to CE & ME)

Time: 3 Hours

Max. Marks: 70

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Note: 1. Question paper consists of two parts (Part-A and Part-B)

2. Answer ALL the question in Part-A

3. Answer any THREE Questions from Part-B

PART – A (14 Marks)

1. a) Define Random variable with example. (2M)
2. b) Write the properties of Normal distribution. (2M)

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3. c) Define Null and Alternative hypothesis. (2M)
4. d) Explain Type-I and Type-II errors. (2M)
5. e) Write the properties of Queueing system. (2M)
6. f) Define Transient and steady state. (2M)
7. g) Define correlation and regression. (2M)

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PART – B (42 Marks)

1. a) A random variable X has the following probability function: (8M)

   x	0	1	2	3	4	5	6	7
   P(x)	0	k	2k	2k	3k	k2	2k2	7k2+k

   (i) Find k (ii) Evaluate P(X<6), P(X=6) and P(0<X<5).

   b) Define Moment generating function. Find the moment generating function of Poisson distribution. (6M)

   OR

   a) If X is a normal variate with mean 30 and standard deviation 5. Find the probabilities that (8M)

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   (i) 26 = X = 40 (ii) X = 45 (iii) |X – 30| > 5

   b) Define continuous probability distribution and write properties of exponential distribution. (6M)

2. a) A population consists of the four numbers 3, 7, 11, 15. Consider all possible samples of size 2 which can be drawn without replacement from the population. Find the population mean and standard deviation, and mean and standard deviation of the sampling distribution of means. (8M)

   b) Explain about point estimation and interval estimation. (6M)

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   OR

   a) A random sample of size 100 is taken from a population with s = 8. Given that the sample mean is x¯ = 82. (8M)

   (i) Determine a 95% confidence interval for the population mean µ.

   (ii) What can we assert with 95% confidence about the possible size of our error if we estimate µ by x¯ = 82.

   b) Explain different types of errors in sampling. (6M)

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3. a) The mean life time of 200 bulbs manufactured by a company is found to be 1500 hours with a standard deviation of 60 hours. Test the hypothesis that the average lifetime of the bulbs is 1550 hours. (8M)

   b) Explain about test of hypothesis for large samples. (6M)

   OR

   a) Two random samples drawn from two normal populations are: (8M)

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   Sample 1: 20 16 26 27 22 18 24 25 19

   Sample 2: 27 33 42 35 32 34 38 28 41 43

   Test whether the populations have the same variance.

   b) Explain about t-test for single mean. (6M)

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4. a) In a bank, 8 customers arrive on an average of every 10 minutes. Find the probability that (8M)

   (i) No customer arrives

   (ii) Exactly 5 customers arrive in a given 1 minute. Assume Poisson distribution.

   b) Write the applications of queuing theory. (6M)

   OR

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   a) A single-server queuing system has a Poisson input with mean arrival rate of 1 customer per minute. It is found that it takes an average of 30 seconds to serve a customer. Assuming that the length of the queue is unlimited, find (8M)

   (i) The probability that an arriving customer will have to wait before being served.

   (ii) The average number of customers in the system.

   (iii) The average time a customer spends in the system.

   b) Explain about M/M/1 queuing model. (6M)

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5. a) Calculate the coefficient of correlation and obtain the lines of regression for the following data: (8M)

   X	1	2	3	4	5	6	7	8	9
   Y	9	8	10	12	11	13	14	16	15

   b) Explain about properties of regression coefficients. (6M)

   OR

   a) The following data relate to the marks in subjects A and B in a certain examination: (8M)

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   Mean marks in A = 36

   Mean marks in B = 85

   Standard deviation of A = 11

   Standard deviation of B = 8

   Coefficient of correlation between A and B = + 0.66

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   (i) Determine the two equations of regression.

   (ii) Estimate the marks in A when the marks in B are 75.

   b) Explain about Scatter diagram. (6M)

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