EE_364_Midterm__2_2010
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EE_364_Midterm__2_2010

Course Number: EE 364, Spring 2011

College/University: USC

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J. M. Mendel Spring 2010 EE 364 Midterm # 2 Closed Book Two 81/2X11 sheet of notes (both sides) permitted Calculator required Tables A.1, A.2 and A.3 required To receive full credit you must carry out all of the numerics x 1. (20 points) For parts a and b, it is true that: X a. (4 points) E (Y ) = ? n( x; , ) and y = 4 +2. 2 b. (4 points) Y = ? c. (12 points) Consider a ferry that can carry both buses and...

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M. J. Mendel Spring 2010 EE 364 Midterm # 2 Closed Book Two 81/2X11 sheet of notes (both sides) permitted Calculator required Tables A.1, A.2 and A.3 required To receive full credit you must carry out all of the numerics x 1. (20 points) For parts a and b, it is true that: X a. (4 points) E (Y ) = ? n( x; , ) and y = 4 +2. 2 b. (4 points) Y = ? c. (12 points) Consider a ferry that can carry both buses and cars on a trip across a waterway. Each trip costs the owner $10. The fee for cars is $3 and the fee for buses is $8. Let X and Y denote the number of buses and cars, respectively, carried on a given trip. The joint distribution of X and Y is given by: y 0 1 2 3 4 5 0 0.01 0.03 0.03 0.07 0.12 0.08 x 1 0.01 0.08 0.06 0.07 0.04 0.06 2 0.03 0.07 0.06 0.13 0.03 0.02 Compute the expected profit for the ferry trip. 2. (20 points) Hospital administrators in large cities anguish about problems with traffic in emergency rooms in hospitals. For a particular hospital in a large city, the staff on hand cannot accommodate the patient traffic if there are more than 10 emergency cases in a given hour. It is assumed that the patient arrival follows a Poisson process and historical data suggest that, on average, 5 emergencies arrive per hour. a. (10 points) What is the that probability in a given hour the staff can no longer accommodate the traffic? b. (10 points) What is the probability that more than 20 emergencies arrive during a 3-hour shift of personnel? 3. (20 points) A soft drink machine is regulated so that it discharges an average of 200 milliliters per cup. If the amount of the drink is normally distributed with a standard deviation equal to 15 milliliters: a. (10 points) Approximately, how many cups will probably overflow if 230 milliliter cups are used for the next 1000 drinks? b. (10 points) To two significant figures, below what value of milliliters do we get the smallest 25% of the drinks? J. M. Mendel Spring 2010 4. (20 points) 100 electrical switches are installed in different systems. The life, in years, of the switch has an exponential distribution with an average life of 2 years. What is the probability that at most 30 switches fail during the first year? 5. (20 points) An electrical firm manufactures a 100-watt light bulb, which, according to the specifications written on the package, has a mean life of 900 hours with a standard deviation of 50 hours. At most, what percentage of bulbs fail to last even 700 hours? Assume that the distribution is symmetric about the mean. [Hint: Use the Chebyshev Theorem.]

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