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Handout9 - of X 2 For Example 3 ±nd E Y 3 For Example 1...

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STOR 435 Handout 9 Sections 5.1-5.3 Example 1 (Example 1a; Continuous rv) . Suppose X is a random variable whose pdf is given by f ( x ) = braceleftbigg C (4 x - 2 x 2 ) 0 <x< 2 0 otherwise 1. Find C 2. What is P ( X > 1)? 3. What is P ( X = 1)? Example 2 (Example 1c; Continuous rv) . The lifetime in hours of a particular radio tube is a random variable having pdf f ( x ) = braceleftbigg 0 x 100 100 /x 2 x> 100 Suppose a radio has 5 tubes, the lifetime of each of the radio tubes having the above distribution. What is the probability that exactly 2 out of the 5 radio tubes will have to be replaced within the first 150 hours of operation? You can assume that E i ,i = 1 , 2 , 3 , 4 , 5, the events that the i th tube has to be replaced within 150 hours are independent of each other. Example 3. For a particular computer component, the lifetime of the compo- nent in hours is known to have density f ( x ) = 10 <x< 1 Let the random variable Y = e X . What is the pdf of Y ? Example 4 (Expectations)
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Unformatted text preview: of X 2. For Example 3, ±nd E ( Y ) 3. For Example 1 ±nd var ( X ) Example 5 (Exercise 5.10; Uniform distribution) . Trains headed for destina-tion A arrive at the train station at 15- minute intervals starting at 7 A. M., whereas trains headed for destination B arrive at 15-minute intervals starting at 7: 05 A. M. 1 1. If a certain passenger arrives at the station at a time uniformly distributed between 7 and 8 A. M. and then gets on the Frst train that arrives, what proportion of time does he or she go to destination A? 2. What if the passenger arrives at a time uniformly distributed between 7: 10 and 8: 10 A. M.? 3. ±or part(a) if X denotes the number of minutes after 7 that the passenger arrives what is E ( X )? What is var ( X )? 2...
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