Download AKTU B-Tech 8th Sem 2014-15 ECS 801 Artificial Intelligence Question Paper

VASAVI COLLEGE OF ENGINEERING (Autonomous), HYDERABAD

B.E. (ECE) VI Semester

Probability Theory and Stochastic Processes (Open Elective - II)

Time: 3 hours Max. Marks: 60

Note: Answer all questions from Part A and Part B.

Part A (10 x 2 = 20 Marks)

1. Define probability and write its properties.

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2. State Bayes’ theorem.
3. What are the properties of joint distribution function?
4. Define marginal distribution function.
5. What is the central limit theorem?
6. Write the properties of auto correlation function.

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7. Define cross-power density spectrum.
8. What is the relation between power spectral density and auto correlation?
9. Define white noise process.
10. Write any two properties of a linear time-invariant system.

Part B (4 x 10 = 40 Marks)

1. (a) In a bolt factory, machines A, B and C manufacture respectively 25, 35 and 40 percent of the total. Of their output 5, 4, and 2 percent are defective bolts. A bolt is drawn at random from the product and is found to be defective. What are the probabilities that it was manufactured by machines A, B and C?

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   OR

   (b) The average number of telephone calls / minute coming into a switch board is 2. Determine the probability that one particular minute there will be (i) 3 or fewer calls (ii) more than 3 calls.

2. (a) Define the joint probability density function. Also explain the properties of joint probability density function.

   OR

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   (b) Two random variables X and Y have joint PDF
   f_xy(x,y) = k(x+y), 0 = x = 1, 0 = y = 1. Find i) k ii) Marginal densities of X and Y.

3. (a) Explain the classification of Random process.

   OR

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   (b) Consider the random process X(t) = A cos(?t + ?) where A and ? are constants and ? is a uniform random variable over (0, 2p). Find whether the process is WSS or not.

4. (a) The power spectral density of a stationary random process is given by S_xx(?) =

   1. |?| , |?| < 1
   2. 0, otherwise

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   Find the auto correlation function.

   OR

   (b) Find the power spectral density of WSS random process whose auto correlation function is R_xx(t) = Ae^-a|t|, where A and a are constants.

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