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Unformatted text preview: 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 & & & & > <- = 5 , 1 5 1...
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This note was uploaded on 01/27/2010 for the course ECE 600 taught by Professor Staff during the Fall '08 term at Purdue University-West Lafayette.
- Fall '08