Similarly the right limit of f at x denoted by f x is

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Unformatted text preview: with a little more work. Four errors go undetected if and only if they are at the intersection points of two columns and two rows. There are 8 = 28 2 ways to choose two columns and 8 = 28 ways to choose two rows, so there are 282 = 784 error 2 patterns with four errors that go undetected. The probability of any given one of those patterns occurring is less than p4 , so by the union bound, the probability that the actual error pattern is an undetected pattern of four bit errors is less than or equal to (784)p4 . Any pattern of five bit errors is detected because any pattern with an odd number of bit errors is detected. So the only other way undetected errors can occur is if Y ≥ 6, and P {Y ≥ 6} can again be bounded by the union bound. Thus, P (undetected errors) ≤ 8 2 2 10−12 + 64 10−18 6 = (784 + 74.974368)10−12 ≤ (0.859)10−9 . 2.12.5 Reliability of a single backup Suppose there are two machines (such as computers, generators, vehicles, etc.) each used to back up the other. Suppose each day, given a machine was up the...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.

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