sol_hw5 - ECE340 spring 2010 Homework- 5 Solutions...

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ECE340 spring 2010 Homework- 5 Solutions Problems: 3-1.2, 3-1.3(b), 3-2.1, 3-2.2, 3-2.3, 3-2.4, 3-3.1, 3-3.3 3-1.2 a) In this problem our joint pdf is: To determine the value k , we need the following condition: Or, From this condition above, we find The joint pdf is therefore: b) To determine the cdf , we use the following equation: We find the cdf as the following: c) We formulate the probability as the following: 1
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d) The marginal density function is the following: 3-1.3 (b) For the random variables of Problem 3-1.2 , the expected value of the product of X and Y is the following: 3-2.1 a) Since the signal X is Rayleigh distributed, we know the pdf of X as the following: Since the mean value of X is 10, according to the page 80, we have the following: So, we know Now, the pdf of signal X is the following: Now, the noise N is uniformly distributed, it is straightforward to find the pdf of N as the following: We also know that X and N are statistically independent and we have an observation as: Since we know that the conditional pdf 2
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This note was uploaded on 06/16/2010 for the course EE e3180 taught by Professor Burl during the Spring '08 term at Michigan Technological University.

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sol_hw5 - ECE340 spring 2010 Homework- 5 Solutions...

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