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# homework2 - COMER ECE 600 Homework 2 1 Let A and B be two...

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C OMER ECE 600 Homework 2 1. Let A and B be two events in a probability space. a. Show that if A and B are independent, then A c and B are also independent. b. If A and B are independent, are they mutually exclusive? Explain. c. Show that if P(A|B) > P(A), then P(B|A) > P(B). 2. If A, B, and C are events in a probability space, show that P(A ° B ° C) = P(A|B ° C)P(B|C)P(C). 3. An experiment consists of picking one of two urns at random, with the two urns being equally likely, and then selecting a ball from the urn and noting its color (black or white). Let A be the event “urn 1 is selected” and B the event “a black ball is selected.” Under what conditions are the events A and B independent? 4. There are two servers at the gorcery store. Server 1 can take anywhere from 1 to 5 minutes to complete an order. Server 2 can take anywhere from 1 to 10 minutes to complete an order. Let T S denote the service time. You are given that ° ° ± ° ° ² ³ > < - = 5 , 1 5 1 , 4 1 1 , 0 1) Server | P(T S t t t t t ° ° ± ° ° ² ³ >

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homework2 - COMER ECE 600 Homework 2 1 Let A and B be two...

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