Fall10_Final_sol

Fall10_Final_sol - 1 The Hong Kong University of Science...

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Unformatted text preview: 1 The Hong Kong University of Science and Technology Department of Electronic and Computer Engineering ELEC 210: Probability and Random Processes in Electrical Engineering 2010 Fall Semester Final Examination December 14, 2010 Name: Student ID: Instructions: 1. This is a 3-hour test. 2. You may use a non-programmable calculator. 3. You may use 1 A4 sheet of your own notes (double-sided). 4. There are 2 sections : a. Section 1: 10 Multiple Choice Questions b. Section II: 6 Problems 5. Try to attempt all questions. 6. Answer each question in your Answer Booklet . 7. The distribution of marks is shown in the table below: Question Mark Multi. Choice 10 1 6 2 7 3 6 4 7 5 7 6 7 Total 50 2 SECTION I: Multiple Choice [10 Marks] Notes:  For each multiple-choice question below, select only ONE answer.  Write your answer in your ANSWER BOOKLET (not this question sheet) [1 Mark Per Question] 1. Which of the following statements about two random variables, X and Y , is not true: a) The correlation of X and Y is symmetrical. b) The covariance of X and Y is symmetrical. c) The correlation coefficient of X and Y is symmetrical. d) The covariance and correlation have the same units. e) The covariance and correlation coefficient have the same units. 2. Which of the following statements is true: a) Correlation of X and Y gives a meaningful measure of how much X and Y vary together. b) Scaling X or Y by a constant does not change their covariance. c) Scaling X or Y by a constant does not change their correlation. d) Scaling X or Y by a constant does not change their correlation coefficient. e) None of the above. 3. Consider the following communication system: A transmitter sends a binary value B to a receiver. The received signal is R = B + N , where N denotes independent random noise obeying a Gaussian distribution. Based on R , the receiver successfully decodes B with probability p ; otherwise it makes a mistake and the transmitter tries again. Let n be the number of times that B must be transmitted before it is received successfully. Which of the following is not true: a) Conditioned on B , the received signal R is a Gaussian random variable. b) Conditioned on B , the received signal R has zero-mean. c) Conditioned on N , the received signal R is a Bernoulli random variable. d) The received signal R is a continuous random variable. e) n is a geometric random variable. 4. Assume that Y 1 , Y 2 , Y 3 are i.i.d. jointly Gaussian random variables. Identify which of the following is not true: a) Y 1 and Y 3 are jointly Gaussian distributed. b) Conditioned on Y 2 , Y 1 and Y 3 are jointly Gaussian distributed. c) For constants a , b, and c , the variable aY 1 + bY 2 + c is Gaussian distributed....
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Fall10_Final_sol - 1 The Hong Kong University of Science...

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