Download AKTU B-Tech 4th Sem 2014-15 Analog And Digital Electronics Question Paper

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

R18 B.Tech II Year II Semester Examinations, November/December - 2020

PROBABILITY AND STATISTICS

(Common to CE, EEE, ME, ECE, CSE, EIE, IT, MCT, ETM, MMT, AE, MIE, PTM, CEE)

--- Content provided by‌ FirstRanker.com ---

Time: 3 Hours 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.

PART - A (25 Marks)

1. a) Define conditional probability. [2M]

--- Content provided by FirstRanker.com ---

2. b) Find the moment generating function of a random variable X having density function
   f(x) = { x, 0 = x = 1
   2-x, 1 = x = 2 [3M]
3. c) Write properties of normal distribution. [2M]
4. d) Define critical region. [3M]

--- Content provided by FirstRanker.com ---

5. e) Write properties of t-distribution. [2M]
6. f) Define type-I and type-II errors. [3M]
7. g) Write the difference between correlation and regression. [2M]
8. h) What is multiple regression? [3M]
9. i) Define transient and steady state. [2M]

--- Content provided by‌ FirstRanker.com ---

10. j) Define queue length and waiting time. [3M]

PART - B (50 Marks)

(Answer all five units, choosing one question from each unit. Each question carries 10 marks.)

UNIT - I

1. 2. a) State and prove Baye's theorem. [5M]
   b) A bag contains 5 white and 3 black balls and a second bag contains 3 white and 2 black balls. A ball is drawn at random from the first bag and placed in the second bag. Then a ball is drawn at random from the second bag. What is the probability that it is a white ball? [5M]

   OR

--- Content provided by‌ FirstRanker.com ---

2. 3. a) A random variable X has the following probability function:
   X : 0 1 2 3 4 5 6 7 8
   P(x): a 3a 5a 7a 9a 11a 13a 15a
   (i) Determine ‘a’ (ii) P(X < 3) (iii) P(X = 3) (iv) P(0 < X < 5) [5M]
   b) The mean and variance of a binomial distribution are 4 and 4/3 respectively. Find P(X = 1). [5M]

--- Content provided by FirstRanker.com ---

UNIT - II

1. 4. a) Show that for the exponential distribution f(x) = (1/s)e^-(x/s), x = 0, s > 0, mean = standard deviation. [5M]
   b) In a normal distribution, 31% of the items are under 45 and 8% are over 64. Find the mean and standard deviation of the distribution. [5M]

   OR

2. 5. a) Define sampling distribution and standard error. [5M]
   b) A population consists of 5 numbers 3, 6, 9, 12, 15. Consider all possible samples of size 2 which can be drawn with replacement from the population. Find:
   

   --- Content provided by⁠ FirstRanker.com ---

   (i) The mean of the population.
   (ii) The standard deviation of the population.
   (iii) The mean of the sampling distribution of means.
   (iv) The standard deviation of the sampling distribution of means. [5M]

UNIT - III

1. 6. A sample of 64 students has a mean weight of 70 kgs. Compared with the population mean of 65 kgs. With a standard deviation of 25 kgs. Is there sufficient evidence to conclude that the students are a heavy group at 5% level of significance. [10M]

   OR

   --- Content provided by‌ FirstRanker.com ---

2. 7. Two independent samples of sizes 9 and 7 from a normal population had means 16 and 13 units respectively and standard deviations 3 and 4 units respectively. Is it reasonable to say that two samples have come from the same population. [10M]

UNIT - IV

1. 8. Calculate the coefficient of correlation and the lines of regression for the following data:
   X : 1 2 3 4 5 6 7
   Y : 9 8 10 12 11 13 14 [10M]

   OR

   --- Content provided by‌ FirstRanker.com ---

2. 9. The heights of fathers and their sons are given below:
   Fathers (in inches) : 65 66 67 67 68 69 70 72
   Sons (in inches) : 67 68 65 68 72 72 69 71
   Find the regression equations of (i) y on x and (ii) x on y. [10M]

--- Content provided by‌ FirstRanker.com ---

UNIT - V

1. 10. a) Explain about queuing problem. [5M]
   b) In a railway yard, goods trains arrive at a rate of 30 trains per day. Assuming that the inter-arrival time follows an exponential distribution and the service time distribution is also exponential with an average of 36 minutes. Calculate the average number of trains in the queue. [5M]

   OR

2. 11. A tax consulting firm has 3 counters. Arrivals are as per Poisson distribution with an average time of 15 minutes between one arrival and the next. Each tax advisor spends 8 minutes on an average for an arrival. If the advisors are paid Rs. 200 per hour, find:
   (i) The average number of customers in the system.
   

   --- Content provided by FirstRanker.com ---

   (ii) The average waiting time of a customer.
   (iii) The hourly cost of the firm to maintain the stated service level. [10M]

---oo0oo---

Get more previous year question papers at: FirstRanker.com

--- Content provided by‌ FirstRanker.com ---