Problem 2: Two Gaussian random variables X and Y are generated independently accord- ing to the same distribution. (Thus

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Problem 2 Two Gaussian Random Variables X And Y Are Generated Independently Accord Ing To The Same Distribution Thus 1 (106.16 KiB) Viewed 60 times

Problem 2: Two Gaussian random variables X and Y are generated independently accord- ing to the same distribution. (Thus, they have exactly the same mean y, and the same variance 02.) (a) What is the probability that X is greater than 0? [Express your answer in terms of the 0(.) function, which is the cdf of the standard Gaussian random variable.] ANSWER: (b) What is the probability X is greater than Y? ANSWER: Problem 3: Assume that we send the information bit sequence “0110" through a channel encoder that uses a (5,1)-repetition code. The output of the channel encoder is connected to a Binary Symmetric Channel (BSC) with crossover probability 0.3. The output of the BSC is connected to a Majority Decoder as the channel decoder. (a) What is the sequence of bits that appear as the input to the BSC? ANSWER: (b) Assume that, in a particular realization, the BSC flips ONLY the 2nd, 3rd and 4th bits of your answer to Part (a). (The remaining bits of the input of the BSC in your answer to Part (a) remain the same.) Find the sequence of bits at the output of the Majority Decoder. ANSWER: