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homework04

# homework04 - Probability for Engineering Applications...

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Probability for Engineering Applications Assignment #4, due at the beginning of class on Thursday, February 16 th , 2006 1. (1 pt) (Textbook exercise 2.64) Let A and B be two events with probabilities P [ A ] and P [ B ]. a. Find P [ A B ] if A and B are independent. b. Find P [ A B ] if A and B are mutually exclusive. 2. (2 pts) Consider a radar system which can be in two conditions: state A representing it is working properly and state ¯ A representing it is not working properly. The probabilities associated with the states changing from one to the other after one unit of time are shown in Figure 1. The arrows in the figure represent the conditional probabilities, for example, the number associated arrow from state A to state ¯ A represents the probability P [ ¯ A | A ] and the the number associated arrow from state A to state A represents the probability P [ A | A ]. Find a. P [ A ]. b. P [ ¯ A ]. _ A A 0.50 0.50 0.30 0.70 Figure 1: State transition disgram 3. (2 pts) (Textbook exercise 2.76) A machine makes errors in a certain operation with probability p . There are two types of errors. The fraction of all errors that are type 1 is

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