HOMEWORK 1-16 - HOMEWORK 1 Winter 2016 Due date Monday...

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HOMEWORK 1 Winter 2016 Due date: Monday January 25 at 4 pm. 1. A binary communication system transmits a signal X that is either 2 + or 2 volts. A malicious channel reduces the magnitude of the received signal by the number of heads it counts in two tosses of a coin. Let Y be the resulting signal. a) Describe the sample space (all possible outcomes) at the receiver. b) Find the set of outcomes corresponding to the event “the transmitted signal was definitely a 2 + ”. c) Describe in words the event corresponding to 0 Y = . 2. Suppose the events A , B , and C are not mutually exclusive. Use appropriate arguments to show that ( ) ( ) ( ) ( ) P A B C P A P B P C + + . 3. A number x is selected at random in the interval [ 1, 2] . Let the events { 0} A x = < , {| 0.5| 0.5} B x = < , and { 0.75} C x = > . a) Find the probabilities of A , B , A B , and A C . b) Compute the probability of A B C . 4. How many seven-digit telephone numbers are possible if the first number is not allowed to be 0 or 1?
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