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(a) Find the mean and variance of y using the above relation. (b) Now generate 500, 1000, and 10000 realizations (trials) of the random variable x using randn() functic the mean and variance of x for different number of realizations. Then, again using the equations 1 an the mean and variance of y. (c) Now compare the mean and variance values of y calculated in (b) for different number of realization theoretical mean and variance values of y calculated in part (a). Comment on the effect of number c e.g., do you have a more accurate estimate of the mean and variance of y as the number of realizations

(a) Find the mean and variance of y using the above relation. (b) Now generate 500, 1000, and 10000 realizations (trials) of the random variable x using randn() functic the mean and variance of x for different number of realizations. Then, again using the equations 1 an the mean and variance of y. (c) Now compare the mean and variance values of y calculated in (b) for different number of realization theoretical mean and variance values of y calculated in part (a). Comment on the effect of number c e.g., do you have a more accurate estimate of the mean and variance of y as the number of realizations

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Suppose that y = x + 3, where x and y are normally distributed random variables. The mean and variance of x are Ha = 10 and o² = 4, thus, x can be generated using randn() command in MATLAB. The mean and variance of y are denoted by µy and o?. If a random variable is a sum of another random variable and a constant, its mean can be calculated as, Hy = µx +3 (1) and the variance remains the same, thus, (2) (a) Find the mean and variance of y using the above relation. (b) Now generate 500, 1000, and 10000 realizations (trials) of the random variable x using randn() function, and obtain the mean and variance of x for different number of realizations. Then, again using the equations 1 and 2, calculate the mean and variance of y. (c) Now compare the mean and variance values of y calculated in (b) for different number of realizations of x, to the theoretical mean and variance values of y calculated in part (a). Comment on the effect of number of realizations, e.g., do you have a more accurate estimate of the mean and variance of y as the number of realizations is increased?
Transcribed Image Text:Suppose that y = x + 3, where x and y are normally distributed random variables. The mean and variance of x are Ha = 10 and o² = 4, thus, x can be generated using randn() command in MATLAB. The mean and variance of y are denoted by µy and o?. If a random variable is a sum of another random variable and a constant, its mean can be calculated as, Hy = µx +3 (1) and the variance remains the same, thus, (2) (a) Find the mean and variance of y using the above relation. (b) Now generate 500, 1000, and 10000 realizations (trials) of the random variable x using randn() function, and obtain the mean and variance of x for different number of realizations. Then, again using the equations 1 and 2, calculate the mean and variance of y. (c) Now compare the mean and variance values of y calculated in (b) for different number of realizations of x, to the theoretical mean and variance values of y calculated in part (a). Comment on the effect of number of realizations, e.g., do you have a more accurate estimate of the mean and variance of y as the number of realizations is increased?
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