Download PTU B.Tech 2021 Jan ECE 5th Sem 78708 Random Variables And Stochastic Processes Question Paper

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Total No. of Pages : 02
Total No. of Questions : 18

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B.Tech. (ECE)(Sem.-5)

RANDOM VARIABLES AND STOCHASTIC PROCESSES
Subject Code : BTEC-905B-18
M.Code : 78708
Time : 3 Hrs. Max. Marks : 60

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INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.

SECTION-A

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Write briefly:

1. Define probability Distribution function
2. What are the conditions for a function to be a random variable?
3. State the importance of central limit theorem.
4. List various levels of stationary random process.

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5. Derive expression for mean for uniform random variable.
6. Explain ergodic random process in short.
7. a) Write a short note on ergodicity.
   b) Write a short note on sampling models
8. Define covariance with example.

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9. Differentiate between Random Processes and Random variables with an example.
10. Write a short note on sets operation.

SECTION-B

11. Explain about conditional probability and its properties.
12. Define power density spectrum and write down its properties.

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13. What is random process? Explain Gaussian random process.
14. Explain the moments of the random variable in detail.
15. Calculate the variance of g(x) = 2x+3 where x is a random variable with probability distribution as :
    
    
    

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    x	0	1	2	3
    	1/4	1/8	1/2	1/8

SECTION-C

16. Discuss random sequences and modes of convergence in detail.
17. State and prove Chebyshev inequality.
18. Describe in detail strong and weak laws of large numbers.

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