This preview shows page 1. Sign up to view the full content.
Unformatted text preview: : Pr[A ∩ B] is 0, but Pr[A] × Pr[B] cannot be 0 since both events have non zero
(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...
View Full Document
This document was uploaded on 01/28/2014.
- Winter '09