midterm2sol

Midterm2sol

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Unformatted text preview: : Pr[A ∩ B] is 0, but Pr[A] × Pr[B] cannot be 0 since both events have non zero probability. (h) (5 points) Suppose Alice wants to send Bob a message consisting of n = 3 characters, and there can be k = 2 general errors during the transmission. So Alice uses an error correcting code and sends Bob n + 2k = 7 characters. Unfortunately, Bob doesn’t receive one of the characters, so he now holds 6 characters. There are still k general errors among the remaining characters, but fortunately Alice managed to tell Bob where one of these general errors is. Since he can now throw away the character with an error, Bob holds only 5 characters. Can Bob still recover Alice’s message? If so, does he need to use all 5 of his remaining characters, or can he use a smaller number? Yes, using 5 characters No Solution: There are now k − 1 = 1 general errors and Alice wants to send a message of n = 3 characters, so n + 2(k − 1) = 5 characters are required. (i) (5 points) A manufacturer claims that they have an excellent test for steroid use. A steroid user tests positive with probability p and non-users test negative with the same probability. It is widely known that the fraction of NCAA football players who use steroids is q. How effective is the test when applied to NCAA football players. i.e. what is the pr...
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This document was uploaded on 01/28/2014.

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