EE 351K Probability and Random Processes FALL 2010 Instructor: Haris Vikalo [email protected]Homework 2 Due on : Tuesday 09/14/10 Problem 1 Bob, Carol, Ted and Alice take turns (in that order) tossing a coin with probability of tossing a Head, P ( H ) = p , where0 < p < 1 . The ﬁrst one to toss a Head wins the game. Calculate P ( B ) , P ( C ) , P ( T ) , and P ( A ) , the win probabilities for Bob, Carol, Ted and Alice, respectively. Also show that • P ( B ) > P ( C ) > P ( T ) > P ( A ) . • P ( B ) + P ( C ) + P ( T ) + P ( A ) = 1 . Problem 2 A new test has been developed to determine whether a given student is overstressed. This test is 90% accurate if the student is not overstressed, but only 80% accurate if the student is overstressed. It is known that 60% of all students are over-stressed. Given that a particular student tests negative for stress, what is the probability that the test result is correct? Problem 3
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